/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 247 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), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 2570 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) NarrowingProof [BOTH BOUNDS(ID, ID), 391 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 10 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 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), 18 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (64) CdtProblem (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 1 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 82 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 17 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 140 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 16 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 143 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 119 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 97 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 194 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms] (162) CdtProblem (163) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 69 ms] (166) CdtProblem (167) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 20 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 61 ms] (170) CdtProblem (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 244 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 260 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 16 ms] (180) 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(and(tt, X)) -> mark(X) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0)) -> mark(0) active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0) -> active(0) mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(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(tt) -> tt encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(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(and(tt, X)) -> mark(X) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0)) -> mark(0) active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0) -> active(0) mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(X1, X2) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(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(and(tt, X)) -> mark(X) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0)) -> mark(0) active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0) -> active(0) mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(X1, X2) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(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(and(tt, X)) -> mark(X) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0)) -> mark(0) active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0) -> active(0) mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(X1, X2) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(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(and(tt, X)) -> mark(X) active(plus(N, 0')) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0')) -> mark(0') active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0') -> active(0') mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(X1, X2) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(0') -> 0' encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: active(and(tt, X)) -> mark(X) active(plus(N, 0')) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0')) -> mark(0') active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0') -> active(0') mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(X1, X2) encArg(tt) -> tt encArg(0') -> 0' encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) Types: active :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x and :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x tt :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x mark :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x plus :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x 0' :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x s :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x x :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encArg :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_active :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_mark :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_and :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_plus :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_s :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_x :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_active :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_and :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_tt :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_mark :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_plus :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_0 :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_s :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_x :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x hole_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x1_3 :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3 :: Nat -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: active, mark, s, plus, x, and, encArg They will be analysed ascendingly in the following order: active = mark s < active plus < active x < active active < encArg s < mark plus < mark x < mark and < mark mark < encArg s < encArg plus < encArg x < encArg and < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: active(and(tt, X)) -> mark(X) active(plus(N, 0')) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0')) -> mark(0') active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0') -> active(0') mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(X1, X2) encArg(tt) -> tt encArg(0') -> 0' encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0' encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) Types: active :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x and :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x tt :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x mark :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x plus :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x 0' :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x s :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x x :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encArg :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_active :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_mark :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_and :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_plus :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_s :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_x :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_active :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_and :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_tt :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_mark :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_plus :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_0 :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_s :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_x :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x hole_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x1_3 :: tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3 :: Nat -> tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x Generator Equations: gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3(0) <=> tt gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3(+(x, 1)) <=> cons_active(gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3(x)) The following defined symbols remain to be analysed: s, active, mark, plus, x, and, encArg They will be analysed ascendingly in the following order: active = mark s < active plus < active x < active active < encArg s < mark plus < mark x < mark and < mark mark < encArg s < encArg plus < encArg x < encArg and < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3(+(1, n507_3))) -> *3_3, rt in Omega(0) Induction Base: encArg(gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3(+(1, 0))) Induction Step: encArg(gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3(+(1, +(n507_3, 1)))) ->_R^Omega(0) active(encArg(gen_tt:0':cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x2_3(+(1, n507_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(and(tt, X)) -> mark(X) active(plus(N, 0)) -> mark(N) active(plus(N, s(M))) -> mark(s(plus(N, M))) active(x(N, 0)) -> mark(0) active(x(N, s(M))) -> mark(plus(x(N, M), N)) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(tt) -> active(tt) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(0) -> active(0) mark(s(X)) -> active(s(mark(X))) mark(x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(mark(X1), X2) -> and(X1, X2) and(X1, mark(X2)) -> and(X1, X2) and(active(X1), X2) -> and(X1, X2) and(X1, active(X2)) -> and(X1, X2) plus(mark(X1), X2) -> plus(X1, X2) plus(X1, mark(X2)) -> plus(X1, X2) plus(active(X1), X2) -> plus(X1, X2) plus(X1, active(X2)) -> plus(X1, X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1), X2) -> x(X1, X2) x(X1, mark(X2)) -> x(X1, X2) x(active(X1), X2) -> x(X1, X2) x(X1, active(X2)) -> x(X1, X2) encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(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(tt) -> active(tt) mark(0) -> active(0) plus(X1, c_mark(X2)) -> plus(X1, X2) s(c_mark(X)) -> s(X) plus(c_mark(X1), X2) -> plus(X1, X2) active(c_x(N, 0)) -> mark(0) active(c_x(N, c_s(M))) -> mark(plus(x(N, M), N)) plus(c_active(X1), X2) -> plus(X1, X2) mark(c_s(X)) -> active(s(mark(X))) x(c_mark(X1), X2) -> x(X1, X2) active(c_and(tt, X)) -> mark(X) s(c_active(X)) -> s(X) x(c_active(X1), X2) -> x(X1, X2) and(c_active(X1), X2) -> and(X1, X2) active(c_plus(N, c_s(M))) -> mark(s(plus(N, M))) and(X1, c_mark(X2)) -> and(X1, X2) x(X1, c_active(X2)) -> x(X1, X2) active(c_plus(N, 0)) -> mark(N) and(c_mark(X1), X2) -> and(X1, X2) mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) plus(X1, c_active(X2)) -> plus(X1, X2) mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) x(X1, c_mark(X2)) -> x(X1, X2) mark(c_x(X1, X2)) -> active(x(mark(X1), mark(X2))) and(X1, c_active(X2)) -> and(X1, X2) The (relative) TRS S consists of the following rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) encode_active(x_1) -> active(encArg(x_1)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_s(x_1) -> s(encArg(x_1)) encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) s(x0) -> c_s(x0) active(x0) -> c_active(x0) plus(x0, x1) -> c_plus(x0, x1) x(x0, x1) -> c_x(x0, x1) and(x0, x1) -> c_and(x0, x1) mark(x0) -> c_mark(x0) Rewrite Strategy: INNERMOST ---------------------------------------- (19) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: mark(tt) -> active(tt) [1] mark(0) -> active(0) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] active(c_x(N, 0)) -> mark(0) [1] active(c_x(N, c_s(M))) -> mark(plus(x(N, M), N)) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] x(c_mark(X1), X2) -> x(X1, X2) [1] active(c_and(tt, X)) -> mark(X) [1] s(c_active(X)) -> s(X) [1] x(c_active(X1), X2) -> x(X1, X2) [1] and(c_active(X1), X2) -> and(X1, X2) [1] active(c_plus(N, c_s(M))) -> mark(s(plus(N, M))) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] x(X1, c_active(X2)) -> x(X1, X2) [1] active(c_plus(N, 0)) -> mark(N) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] x(X1, c_mark(X2)) -> x(X1, X2) [1] mark(c_x(X1, X2)) -> active(x(mark(X1), mark(X2))) [1] and(X1, c_active(X2)) -> and(X1, X2) [1] encArg(tt) -> tt [0] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] x(x0, x1) -> c_x(x0, x1) [0] and(x0, x1) -> c_and(x0, x1) [0] mark(x0) -> c_mark(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(tt) -> active(tt) [1] mark(0) -> active(0) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] active(c_x(N, 0)) -> mark(0) [1] active(c_x(N, c_s(M))) -> mark(plus(x(N, M), N)) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] x(c_mark(X1), X2) -> x(X1, X2) [1] active(c_and(tt, X)) -> mark(X) [1] s(c_active(X)) -> s(X) [1] x(c_active(X1), X2) -> x(X1, X2) [1] and(c_active(X1), X2) -> and(X1, X2) [1] active(c_plus(N, c_s(M))) -> mark(s(plus(N, M))) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] x(X1, c_active(X2)) -> x(X1, X2) [1] active(c_plus(N, 0)) -> mark(N) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] x(X1, c_mark(X2)) -> x(X1, X2) [1] mark(c_x(X1, X2)) -> active(x(mark(X1), mark(X2))) [1] and(X1, c_active(X2)) -> and(X1, X2) [1] encArg(tt) -> tt [0] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] x(x0, x1) -> c_x(x0, x1) [0] and(x0, x1) -> c_and(x0, x1) [0] mark(x0) -> c_mark(x0) [0] The TRS has the following type information: mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x 0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x c_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x c_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x c_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x c_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x c_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x c_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encArg :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x cons_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x encode_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x Rewrite Strategy: INNERMOST ---------------------------------------- (23) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_active_1 encode_and_2 encode_tt encode_mark_1 encode_plus_2 encode_0 encode_s_1 encode_x_2 s_1 active_1 plus_2 x_2 and_2 mark_1 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_and(v0, v1) -> null_encode_and [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_x(v0, v1) -> null_encode_x [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] x(v0, v1) -> null_x [0] and(v0, v1) -> null_and [0] mark(v0) -> null_mark [0] And the following fresh constants: null_encArg, null_encode_active, null_encode_and, null_encode_tt, null_encode_mark, null_encode_plus, null_encode_0, null_encode_s, null_encode_x, null_s, null_active, null_plus, null_x, null_and, null_mark ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(tt) -> active(tt) [1] mark(0) -> active(0) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] active(c_x(N, 0)) -> mark(0) [1] active(c_x(N, c_s(M))) -> mark(plus(x(N, M), N)) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] x(c_mark(X1), X2) -> x(X1, X2) [1] active(c_and(tt, X)) -> mark(X) [1] s(c_active(X)) -> s(X) [1] x(c_active(X1), X2) -> x(X1, X2) [1] and(c_active(X1), X2) -> and(X1, X2) [1] active(c_plus(N, c_s(M))) -> mark(s(plus(N, M))) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] x(X1, c_active(X2)) -> x(X1, X2) [1] active(c_plus(N, 0)) -> mark(N) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] x(X1, c_mark(X2)) -> x(X1, X2) [1] mark(c_x(X1, X2)) -> active(x(mark(X1), mark(X2))) [1] and(X1, c_active(X2)) -> and(X1, X2) [1] encArg(tt) -> tt [0] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] x(x0, x1) -> c_x(x0, x1) [0] and(x0, x1) -> c_and(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_and(v0, v1) -> null_encode_and [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_x(v0, v1) -> null_encode_x [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] x(v0, v1) -> null_x [0] and(v0, v1) -> null_and [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark 0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encArg :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encArg :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (25) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(tt) -> active(tt) [1] mark(0) -> active(0) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] active(c_x(N, 0)) -> mark(0) [1] active(c_x(c_mark(X1'), c_s(M))) -> mark(plus(x(X1', M), c_mark(X1'))) [2] active(c_x(c_active(X1''), c_s(M))) -> mark(plus(x(X1'', M), c_active(X1''))) [2] active(c_x(N, c_s(c_active(X2')))) -> mark(plus(x(N, X2'), N)) [2] active(c_x(N, c_s(c_mark(X2'')))) -> mark(plus(x(N, X2''), N)) [2] active(c_x(N, c_s(M))) -> mark(plus(c_x(N, M), N)) [1] active(c_x(N, c_s(M))) -> mark(plus(null_x, N)) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(tt)) -> active(s(active(tt))) [2] mark(c_s(0)) -> active(s(active(0))) [2] mark(c_s(c_s(X'))) -> active(s(active(s(mark(X'))))) [2] mark(c_s(c_and(X11, X21))) -> active(s(active(and(mark(X11), X21)))) [2] mark(c_s(c_plus(X12, X22))) -> active(s(active(plus(mark(X12), mark(X22))))) [2] mark(c_s(c_x(X13, X23))) -> active(s(active(x(mark(X13), mark(X23))))) [2] mark(c_s(X)) -> active(s(c_mark(X))) [1] mark(c_s(X)) -> active(s(null_mark)) [1] x(c_mark(X1), X2) -> x(X1, X2) [1] active(c_and(tt, X)) -> mark(X) [1] s(c_active(X)) -> s(X) [1] x(c_active(X1), X2) -> x(X1, X2) [1] and(c_active(X1), X2) -> and(X1, X2) [1] active(c_plus(N, c_s(c_mark(X24)))) -> mark(s(plus(N, X24))) [2] active(c_plus(c_mark(X14), c_s(M))) -> mark(s(plus(X14, M))) [2] active(c_plus(c_active(X15), c_s(M))) -> mark(s(plus(X15, M))) [2] active(c_plus(N, c_s(c_active(X25)))) -> mark(s(plus(N, X25))) [2] active(c_plus(N, c_s(M))) -> mark(s(c_plus(N, M))) [1] active(c_plus(N, c_s(M))) -> mark(s(null_plus)) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] x(X1, c_active(X2)) -> x(X1, X2) [1] active(c_plus(N, 0)) -> mark(N) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] mark(c_and(tt, X2)) -> active(and(active(tt), X2)) [2] mark(c_and(0, X2)) -> active(and(active(0), X2)) [2] mark(c_and(c_s(X''), X2)) -> active(and(active(s(mark(X''))), X2)) [2] mark(c_and(c_and(X16, X26), X2)) -> active(and(active(and(mark(X16), X26)), X2)) [2] mark(c_and(c_plus(X17, X27), X2)) -> active(and(active(plus(mark(X17), mark(X27))), X2)) [2] mark(c_and(c_x(X18, X28), X2)) -> active(and(active(x(mark(X18), mark(X28))), X2)) [2] mark(c_and(X1, X2)) -> active(and(c_mark(X1), X2)) [1] mark(c_and(X1, X2)) -> active(and(null_mark, X2)) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] x(X1, c_mark(X2)) -> x(X1, X2) [1] mark(c_x(X1, X2)) -> active(x(mark(X1), mark(X2))) [1] and(X1, c_active(X2)) -> and(X1, X2) [1] encArg(tt) -> tt [0] encArg(0) -> 0 [0] encArg(cons_active(tt)) -> active(tt) [0] encArg(cons_active(0)) -> active(0) [0] encArg(cons_active(cons_active(x_1'))) -> active(active(encArg(x_1'))) [0] encArg(cons_active(cons_mark(x_1''))) -> active(mark(encArg(x_1''))) [0] encArg(cons_active(cons_and(x_11, x_2'))) -> active(and(encArg(x_11), encArg(x_2'))) [0] encArg(cons_active(cons_plus(x_12, x_2''))) -> active(plus(encArg(x_12), encArg(x_2''))) [0] encArg(cons_active(cons_s(x_13))) -> active(s(encArg(x_13))) [0] encArg(cons_active(cons_x(x_14, x_21))) -> active(x(encArg(x_14), encArg(x_21))) [0] encArg(cons_active(x_1)) -> active(null_encArg) [0] encArg(cons_mark(tt)) -> mark(tt) [0] encArg(cons_mark(0)) -> mark(0) [0] encArg(cons_mark(cons_active(x_15))) -> mark(active(encArg(x_15))) [0] encArg(cons_mark(cons_mark(x_16))) -> mark(mark(encArg(x_16))) [0] encArg(cons_mark(cons_and(x_17, x_22))) -> mark(and(encArg(x_17), encArg(x_22))) [0] encArg(cons_mark(cons_plus(x_18, x_23))) -> mark(plus(encArg(x_18), encArg(x_23))) [0] encArg(cons_mark(cons_s(x_19))) -> mark(s(encArg(x_19))) [0] encArg(cons_mark(cons_x(x_110, x_24))) -> mark(x(encArg(x_110), encArg(x_24))) [0] encArg(cons_mark(x_1)) -> mark(null_encArg) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(tt)) -> s(tt) [0] encArg(cons_s(0)) -> s(0) [0] encArg(cons_s(cons_active(x_1131))) -> s(active(encArg(x_1131))) [0] encArg(cons_s(cons_mark(x_1132))) -> s(mark(encArg(x_1132))) [0] encArg(cons_s(cons_and(x_1133, x_265))) -> s(and(encArg(x_1133), encArg(x_265))) [0] encArg(cons_s(cons_plus(x_1134, x_266))) -> s(plus(encArg(x_1134), encArg(x_266))) [0] encArg(cons_s(cons_s(x_1135))) -> s(s(encArg(x_1135))) [0] encArg(cons_s(cons_x(x_1136, x_267))) -> s(x(encArg(x_1136), encArg(x_267))) [0] encArg(cons_s(x_1)) -> s(null_encArg) [0] encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) [0] encode_active(tt) -> active(tt) [0] encode_active(0) -> active(0) [0] encode_active(cons_active(x_1197)) -> active(active(encArg(x_1197))) [0] encode_active(cons_mark(x_1198)) -> active(mark(encArg(x_1198))) [0] encode_active(cons_and(x_1199, x_298)) -> active(and(encArg(x_1199), encArg(x_298))) [0] encode_active(cons_plus(x_1200, x_299)) -> active(plus(encArg(x_1200), encArg(x_299))) [0] encode_active(cons_s(x_1201)) -> active(s(encArg(x_1201))) [0] encode_active(cons_x(x_1202, x_2100)) -> active(x(encArg(x_1202), encArg(x_2100))) [0] encode_active(x_1) -> active(null_encArg) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(tt) -> mark(tt) [0] encode_mark(0) -> mark(0) [0] encode_mark(cons_active(x_1263)) -> mark(active(encArg(x_1263))) [0] encode_mark(cons_mark(x_1264)) -> mark(mark(encArg(x_1264))) [0] encode_mark(cons_and(x_1265, x_2131)) -> mark(and(encArg(x_1265), encArg(x_2131))) [0] encode_mark(cons_plus(x_1266, x_2132)) -> mark(plus(encArg(x_1266), encArg(x_2132))) [0] encode_mark(cons_s(x_1267)) -> mark(s(encArg(x_1267))) [0] encode_mark(cons_x(x_1268, x_2133)) -> mark(x(encArg(x_1268), encArg(x_2133))) [0] encode_mark(x_1) -> mark(null_encArg) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(tt) -> s(tt) [0] encode_s(0) -> s(0) [0] encode_s(cons_active(x_1329)) -> s(active(encArg(x_1329))) [0] encode_s(cons_mark(x_1330)) -> s(mark(encArg(x_1330))) [0] encode_s(cons_and(x_1331, x_2164)) -> s(and(encArg(x_1331), encArg(x_2164))) [0] encode_s(cons_plus(x_1332, x_2165)) -> s(plus(encArg(x_1332), encArg(x_2165))) [0] encode_s(cons_s(x_1333)) -> s(s(encArg(x_1333))) [0] encode_s(cons_x(x_1334, x_2166)) -> s(x(encArg(x_1334), encArg(x_2166))) [0] encode_s(x_1) -> s(null_encArg) [0] encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] x(x0, x1) -> c_x(x0, x1) [0] and(x0, x1) -> c_and(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_and(v0, v1) -> null_encode_and [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_x(v0, v1) -> null_encode_x [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] x(v0, v1) -> null_x [0] and(v0, v1) -> null_and [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark 0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encArg :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encArg :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (27) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_encArg => 0 null_encode_active => 0 null_encode_and => 0 null_encode_tt => 0 null_encode_mark => 0 null_encode_plus => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_x => 0 null_s => 0 null_active => 0 null_plus => 0 null_x => 0 null_and => 0 null_mark => 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: active(z) -{ 1 }-> mark(N) :|: z = 1 + N + 0, N >= 0 active(z) -{ 1 }-> mark(X) :|: z = 1 + 1 + X, X >= 0 active(z) -{ 2 }-> mark(s(plus(N, X24))) :|: z = 1 + N + (1 + (1 + X24)), N >= 0, X24 >= 0 active(z) -{ 2 }-> mark(s(plus(N, X25))) :|: X25 >= 0, z = 1 + N + (1 + (1 + X25)), N >= 0 active(z) -{ 2 }-> mark(s(plus(X14, M))) :|: M >= 0, z = 1 + (1 + X14) + (1 + M), X14 >= 0 active(z) -{ 2 }-> mark(s(plus(X15, M))) :|: z = 1 + (1 + X15) + (1 + M), X15 >= 0, M >= 0 active(z) -{ 1 }-> mark(s(0)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(s(1 + N + M)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 2 }-> mark(plus(x(N, X2'), N)) :|: X2' >= 0, z = 1 + N + (1 + (1 + X2')), N >= 0 active(z) -{ 2 }-> mark(plus(x(N, X2''), N)) :|: X2'' >= 0, z = 1 + N + (1 + (1 + X2'')), N >= 0 active(z) -{ 2 }-> mark(plus(x(X1', M), 1 + X1')) :|: X1' >= 0, z = 1 + (1 + X1') + (1 + M), M >= 0 active(z) -{ 2 }-> mark(plus(x(X1'', M), 1 + X1'')) :|: X1'' >= 0, z = 1 + (1 + X1'') + (1 + M), M >= 0 active(z) -{ 1 }-> mark(plus(0, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(plus(1 + N + M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(0) :|: z = 1 + N + 0, N >= 0 active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 active(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 and(z, z') -{ 1 }-> and(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 and(z, z') -{ 1 }-> and(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 and(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> x(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> s(x(encArg(x_1136), encArg(x_267))) :|: x_1136 >= 0, z = 1 + (1 + x_1136 + x_267), x_267 >= 0 encArg(z) -{ 0 }-> s(s(encArg(x_1135))) :|: z = 1 + (1 + x_1135), x_1135 >= 0 encArg(z) -{ 0 }-> s(plus(encArg(x_1134), encArg(x_266))) :|: x_266 >= 0, z = 1 + (1 + x_1134 + x_266), x_1134 >= 0 encArg(z) -{ 0 }-> s(mark(encArg(x_1132))) :|: z = 1 + (1 + x_1132), x_1132 >= 0 encArg(z) -{ 0 }-> s(and(encArg(x_1133), encArg(x_265))) :|: x_1133 >= 0, x_265 >= 0, z = 1 + (1 + x_1133 + x_265) encArg(z) -{ 0 }-> s(active(encArg(x_1131))) :|: z = 1 + (1 + x_1131), x_1131 >= 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 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> mark(x(encArg(x_110), encArg(x_24))) :|: z = 1 + (1 + x_110 + x_24), x_24 >= 0, x_110 >= 0 encArg(z) -{ 0 }-> mark(s(encArg(x_19))) :|: z = 1 + (1 + x_19), x_19 >= 0 encArg(z) -{ 0 }-> mark(plus(encArg(x_18), encArg(x_23))) :|: z = 1 + (1 + x_18 + x_23), x_23 >= 0, x_18 >= 0 encArg(z) -{ 0 }-> mark(mark(encArg(x_16))) :|: x_16 >= 0, z = 1 + (1 + x_16) encArg(z) -{ 0 }-> mark(and(encArg(x_17), encArg(x_22))) :|: x_17 >= 0, z = 1 + (1 + x_17 + x_22), x_22 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(x_15))) :|: x_15 >= 0, z = 1 + (1 + x_15) 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 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> active(x(encArg(x_14), encArg(x_21))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(s(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0 encArg(z) -{ 0 }-> active(plus(encArg(x_12), encArg(x_2''))) :|: z = 1 + (1 + x_12 + x_2''), x_2'' >= 0, x_12 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> active(and(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2') encArg(z) -{ 0 }-> active(active(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 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 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_active(z) -{ 0 }-> active(x(encArg(x_1202), encArg(x_2100))) :|: x_2100 >= 0, z = 1 + x_1202 + x_2100, x_1202 >= 0 encode_active(z) -{ 0 }-> active(s(encArg(x_1201))) :|: x_1201 >= 0, z = 1 + x_1201 encode_active(z) -{ 0 }-> active(plus(encArg(x_1200), encArg(x_299))) :|: x_1200 >= 0, x_299 >= 0, z = 1 + x_1200 + x_299 encode_active(z) -{ 0 }-> active(mark(encArg(x_1198))) :|: z = 1 + x_1198, x_1198 >= 0 encode_active(z) -{ 0 }-> active(and(encArg(x_1199), encArg(x_298))) :|: z = 1 + x_1199 + x_298, x_1199 >= 0, x_298 >= 0 encode_active(z) -{ 0 }-> active(active(encArg(x_1197))) :|: z = 1 + x_1197, x_1197 >= 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_and(z, z') -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_mark(z) -{ 0 }-> mark(x(encArg(x_1268), encArg(x_2133))) :|: x_1268 >= 0, x_2133 >= 0, z = 1 + x_1268 + x_2133 encode_mark(z) -{ 0 }-> mark(s(encArg(x_1267))) :|: z = 1 + x_1267, x_1267 >= 0 encode_mark(z) -{ 0 }-> mark(plus(encArg(x_1266), encArg(x_2132))) :|: x_2132 >= 0, z = 1 + x_1266 + x_2132, x_1266 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(x_1264))) :|: z = 1 + x_1264, x_1264 >= 0 encode_mark(z) -{ 0 }-> mark(and(encArg(x_1265), encArg(x_2131))) :|: x_2131 >= 0, z = 1 + x_1265 + x_2131, x_1265 >= 0 encode_mark(z) -{ 0 }-> mark(active(encArg(x_1263))) :|: x_1263 >= 0, z = 1 + x_1263 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_plus(z, z') -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_s(z) -{ 0 }-> s(x(encArg(x_1334), encArg(x_2166))) :|: x_1334 >= 0, z = 1 + x_1334 + x_2166, x_2166 >= 0 encode_s(z) -{ 0 }-> s(s(encArg(x_1333))) :|: z = 1 + x_1333, x_1333 >= 0 encode_s(z) -{ 0 }-> s(plus(encArg(x_1332), encArg(x_2165))) :|: x_2165 >= 0, z = 1 + x_1332 + x_2165, x_1332 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(x_1330))) :|: z = 1 + x_1330, x_1330 >= 0 encode_s(z) -{ 0 }-> s(and(encArg(x_1331), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + x_1331 + x_2164, x_1331 >= 0 encode_s(z) -{ 0 }-> s(active(encArg(x_1329))) :|: z = 1 + x_1329, x_1329 >= 0 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_tt -{ 0 }-> 1 :|: encode_tt -{ 0 }-> 0 :|: encode_x(z, z') -{ 0 }-> x(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 mark(z) -{ 1 }-> active(x(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(s(active(x(mark(X13), mark(X23))))) :|: z = 1 + (1 + X13 + X23), X13 >= 0, X23 >= 0 mark(z) -{ 2 }-> active(s(active(s(mark(X'))))) :|: X' >= 0, z = 1 + (1 + X') mark(z) -{ 2 }-> active(s(active(plus(mark(X12), mark(X22))))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 2 }-> active(s(active(and(mark(X11), X21)))) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 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 + X, X >= 0 mark(z) -{ 1 }-> active(s(1 + X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(plus(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(and(active(x(mark(X18), mark(X28))), X2)) :|: z = 1 + (1 + X18 + X28) + X2, X18 >= 0, X28 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(s(mark(X''))), X2)) :|: z = 1 + (1 + X'') + X2, X'' >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(plus(mark(X17), mark(X27))), X2)) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> active(and(active(and(mark(X16), X26)), X2)) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 2 }-> active(and(active(1), X2)) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> active(and(active(0), X2)) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 1 }-> active(and(0, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(and(1 + X1, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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 plus(z, z') -{ 1 }-> plus(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 plus(z, z') -{ 1 }-> plus(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 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 x(z, z') -{ 1 }-> x(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 x(z, z') -{ 1 }-> x(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 x(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: active(z) -{ 2 }-> mark(s(plus(N, X24))) :|: z = 1 + N + (1 + (1 + X24)), N >= 0, X24 >= 0 active(z) -{ 2 }-> mark(s(plus(N, X25))) :|: X25 >= 0, z = 1 + N + (1 + (1 + X25)), N >= 0 active(z) -{ 2 }-> mark(s(plus(X14, M))) :|: M >= 0, z = 1 + (1 + X14) + (1 + M), X14 >= 0 active(z) -{ 2 }-> mark(s(plus(X15, M))) :|: z = 1 + (1 + X15) + (1 + M), X15 >= 0, M >= 0 active(z) -{ 1 }-> mark(s(0)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(s(1 + N + M)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 2 }-> mark(plus(x(N, X2'), N)) :|: X2' >= 0, z = 1 + N + (1 + (1 + X2')), N >= 0 active(z) -{ 2 }-> mark(plus(x(N, X2''), N)) :|: X2'' >= 0, z = 1 + N + (1 + (1 + X2'')), N >= 0 active(z) -{ 2 }-> mark(plus(x(X1', M), 1 + X1')) :|: X1' >= 0, z = 1 + (1 + X1') + (1 + M), M >= 0 active(z) -{ 2 }-> mark(plus(x(X1'', M), 1 + X1'')) :|: X1'' >= 0, z = 1 + (1 + X1'') + (1 + M), M >= 0 active(z) -{ 1 }-> mark(plus(0, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(plus(1 + N + M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(0) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(z - 2) :|: z - 2 >= 0 active(z) -{ 1 }-> mark(z - 1) :|: z - 1 >= 0 active(z) -{ 0 }-> 0 :|: z >= 0 active(z) -{ 0 }-> 1 + z :|: z >= 0 and(z, z') -{ 1 }-> and(z, z' - 1) :|: z >= 0, z' - 1 >= 0 and(z, z') -{ 1 }-> and(z - 1, z') :|: z - 1 >= 0, z' >= 0 and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 and(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 encArg(z) -{ 0 }-> x(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> s(x(encArg(x_1136), encArg(x_267))) :|: x_1136 >= 0, z = 1 + (1 + x_1136 + x_267), x_267 >= 0 encArg(z) -{ 0 }-> s(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(plus(encArg(x_1134), encArg(x_266))) :|: x_266 >= 0, z = 1 + (1 + x_1134 + x_266), x_1134 >= 0 encArg(z) -{ 0 }-> s(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(and(encArg(x_1133), encArg(x_265))) :|: x_1133 >= 0, x_265 >= 0, z = 1 + (1 + x_1133 + x_265) encArg(z) -{ 0 }-> s(active(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 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> mark(x(encArg(x_110), encArg(x_24))) :|: z = 1 + (1 + x_110 + x_24), x_24 >= 0, x_110 >= 0 encArg(z) -{ 0 }-> mark(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(plus(encArg(x_18), encArg(x_23))) :|: z = 1 + (1 + x_18 + x_23), x_23 >= 0, x_18 >= 0 encArg(z) -{ 0 }-> mark(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(and(encArg(x_17), encArg(x_22))) :|: x_17 >= 0, z = 1 + (1 + x_17 + x_22), x_22 >= 0 encArg(z) -{ 0 }-> mark(active(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 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> active(x(encArg(x_14), encArg(x_21))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(plus(encArg(x_12), encArg(x_2''))) :|: z = 1 + (1 + x_12 + x_2''), x_2'' >= 0, x_12 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(and(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2') encArg(z) -{ 0 }-> active(active(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 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_0 -{ 0 }-> 0 :|: encode_active(z) -{ 0 }-> active(x(encArg(x_1202), encArg(x_2100))) :|: x_2100 >= 0, z = 1 + x_1202 + x_2100, x_1202 >= 0 encode_active(z) -{ 0 }-> active(s(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(plus(encArg(x_1200), encArg(x_299))) :|: x_1200 >= 0, x_299 >= 0, z = 1 + x_1200 + x_299 encode_active(z) -{ 0 }-> active(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(and(encArg(x_1199), encArg(x_298))) :|: z = 1 + x_1199 + x_298, x_1199 >= 0, x_298 >= 0 encode_active(z) -{ 0 }-> active(active(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_and(z, z') -{ 0 }-> and(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_mark(z) -{ 0 }-> mark(x(encArg(x_1268), encArg(x_2133))) :|: x_1268 >= 0, x_2133 >= 0, z = 1 + x_1268 + x_2133 encode_mark(z) -{ 0 }-> mark(s(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(plus(encArg(x_1266), encArg(x_2132))) :|: x_2132 >= 0, z = 1 + x_1266 + x_2132, x_1266 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(and(encArg(x_1265), encArg(x_2131))) :|: x_2131 >= 0, z = 1 + x_1265 + x_2131, x_1265 >= 0 encode_mark(z) -{ 0 }-> mark(active(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_plus(z, z') -{ 0 }-> plus(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_s(z) -{ 0 }-> s(x(encArg(x_1334), encArg(x_2166))) :|: x_1334 >= 0, z = 1 + x_1334 + x_2166, x_2166 >= 0 encode_s(z) -{ 0 }-> s(s(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(plus(encArg(x_1332), encArg(x_2165))) :|: x_2165 >= 0, z = 1 + x_1332 + x_2165, x_1332 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(and(encArg(x_1331), encArg(x_2164))) :|: x_2164 >= 0, z = 1 + x_1331 + x_2164, x_1331 >= 0 encode_s(z) -{ 0 }-> s(active(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_tt -{ 0 }-> 1 :|: encode_tt -{ 0 }-> 0 :|: encode_x(z, z') -{ 0 }-> x(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_x(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> active(x(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(s(active(x(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(plus(mark(X12), mark(X22))))) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 2 }-> active(s(active(and(mark(X11), X21)))) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 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) -{ 1 }-> active(plus(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> active(and(active(x(mark(X18), mark(X28))), X2)) :|: z = 1 + (1 + X18 + X28) + X2, X18 >= 0, X28 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(s(mark(X''))), X2)) :|: z = 1 + (1 + X'') + X2, X'' >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(plus(mark(X17), mark(X27))), X2)) :|: X17 >= 0, X27 >= 0, z = 1 + (1 + X17 + X27) + X2, X2 >= 0 mark(z) -{ 2 }-> active(and(active(and(mark(X16), X26)), X2)) :|: X16 >= 0, X26 >= 0, z = 1 + (1 + X16 + X26) + X2, X2 >= 0 mark(z) -{ 2 }-> active(and(active(1), z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(and(active(0), z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(and(0, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(and(1 + X1, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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 plus(z, z') -{ 1 }-> plus(z, z' - 1) :|: z >= 0, z' - 1 >= 0 plus(z, z') -{ 1 }-> plus(z - 1, z') :|: z - 1 >= 0, z' >= 0 plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 plus(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 s(z) -{ 1 }-> s(z - 1) :|: z - 1 >= 0 s(z) -{ 0 }-> 0 :|: z >= 0 s(z) -{ 0 }-> 1 + z :|: z >= 0 x(z, z') -{ 1 }-> x(z, z' - 1) :|: z >= 0, z' - 1 >= 0 x(z, z') -{ 1 }-> x(z - 1, z') :|: z - 1 >= 0, z' >= 0 x(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 x(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 ---------------------------------------- (31) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_and(v0, v1) -> null_encode_and [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_x(v0, v1) -> null_encode_x [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] x(v0, v1) -> null_x [0] and(v0, v1) -> null_and [0] mark(v0) -> null_mark [0] And the following fresh constants: null_encArg, null_encode_active, null_encode_and, null_encode_tt, null_encode_mark, null_encode_plus, null_encode_0, null_encode_s, null_encode_x, null_s, null_active, null_plus, null_x, null_and, null_mark ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: mark(tt) -> active(tt) [1] mark(0) -> active(0) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] active(c_x(N, 0)) -> mark(0) [1] active(c_x(N, c_s(M))) -> mark(plus(x(N, M), N)) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] x(c_mark(X1), X2) -> x(X1, X2) [1] active(c_and(tt, X)) -> mark(X) [1] s(c_active(X)) -> s(X) [1] x(c_active(X1), X2) -> x(X1, X2) [1] and(c_active(X1), X2) -> and(X1, X2) [1] active(c_plus(N, c_s(M))) -> mark(s(plus(N, M))) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] x(X1, c_active(X2)) -> x(X1, X2) [1] active(c_plus(N, 0)) -> mark(N) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] x(X1, c_mark(X2)) -> x(X1, X2) [1] mark(c_x(X1, X2)) -> active(x(mark(X1), mark(X2))) [1] and(X1, c_active(X2)) -> and(X1, X2) [1] encArg(tt) -> tt [0] encArg(0) -> 0 [0] encArg(cons_active(x_1)) -> active(encArg(x_1)) [0] encArg(cons_mark(x_1)) -> mark(encArg(x_1)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_x(x_1, x_2)) -> x(encArg(x_1), encArg(x_2)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_0 -> 0 [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_x(x_1, x_2) -> x(encArg(x_1), encArg(x_2)) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] x(x0, x1) -> c_x(x0, x1) [0] and(x0, x1) -> c_and(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_and(v0, v1) -> null_encode_and [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] encode_s(v0) -> null_encode_s [0] encode_x(v0, v1) -> null_encode_x [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] x(v0, v1) -> null_x [0] and(v0, v1) -> null_and [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark 0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark c_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encArg :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark cons_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark encode_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark -> tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encArg :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_tt :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_0 :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_encode_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_s :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_active :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_plus :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_x :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_and :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark null_mark :: tt:0:c_mark:c_x:c_s:c_active:c_and:c_plus:cons_active:cons_mark:cons_and:cons_plus:cons_s:cons_x:null_encArg:null_encode_active:null_encode_and:null_encode_tt:null_encode_mark:null_encode_plus:null_encode_0:null_encode_s:null_encode_x:null_s:null_active:null_plus:null_x:null_and:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_encArg => 0 null_encode_active => 0 null_encode_and => 0 null_encode_tt => 0 null_encode_mark => 0 null_encode_plus => 0 null_encode_0 => 0 null_encode_s => 0 null_encode_x => 0 null_s => 0 null_active => 0 null_plus => 0 null_x => 0 null_and => 0 null_mark => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: active(z) -{ 1 }-> mark(N) :|: z = 1 + N + 0, N >= 0 active(z) -{ 1 }-> mark(X) :|: z = 1 + 1 + X, X >= 0 active(z) -{ 1 }-> mark(s(plus(N, M))) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(plus(x(N, M), N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(0) :|: z = 1 + N + 0, N >= 0 active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 active(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 and(z, z') -{ 1 }-> and(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 and(z, z') -{ 1 }-> and(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 and(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> x(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 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> mark(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> and(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 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0 -{ 0 }-> 0 :|: encode_active(z) -{ 0 }-> active(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_active(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_and(z, z') -{ 0 }-> and(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_mark(z) -{ 0 }-> mark(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_plus(z, z') -{ 0 }-> plus(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_s(z) -{ 0 }-> s(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_s(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_tt -{ 0 }-> 1 :|: encode_tt -{ 0 }-> 0 :|: encode_x(z, z') -{ 0 }-> x(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 mark(z) -{ 1 }-> active(x(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(plus(mark(X1), mark(X2))) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(and(mark(X1), X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 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 plus(z, z') -{ 1 }-> plus(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 plus(z, z') -{ 1 }-> plus(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 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 x(z, z') -{ 1 }-> x(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 x(z, z') -{ 1 }-> x(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 x(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 encode_s(z0) -> s(encArg(z0)) encode_x(z0, z1) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(tt) -> c ENCARG(0) -> c1 ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c8(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_AND(z0, z1) -> c9(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_TT -> c10 ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_0 -> c13 ENCODE_S(z0) -> c14(S(encArg(z0)), ENCARG(z0)) ENCODE_X(z0, z1) -> c15(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), PLUS(x(z0, z1), z0), X(z0, z1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(tt) -> c22(ACTIVE(tt)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c24(ACTIVE(0)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), PLUS(x(z0, z1), z0), X(z0, z1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(tt) -> c22(ACTIVE(tt)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c24(ACTIVE(0)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, and_2, plus_2, s_1, x_2, encArg_1, encode_active_1, encode_and_2, encode_tt, encode_mark_1, encode_plus_2, encode_0, encode_s_1, encode_x_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_TT, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_0, ENCODE_S_1, ENCODE_X_2, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2 Compound Symbols: c, c1, c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_2, c9_3, c10, c11_2, c12_3, c13, c14_2, c15_3, c16_1, c17_1, c18_3, c19_1, c20_3, c21_3, c22_1, c23_4, c24_1, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: ENCODE_TT -> c10 ENCODE_0 -> c13 ENCARG(0) -> c1 ENCARG(tt) -> c ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 encode_s(z0) -> s(encArg(z0)) encode_x(z0, z1) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(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_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c8(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_AND(z0, z1) -> c9(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c14(S(encArg(z0)), ENCARG(z0)) ENCODE_X(z0, z1) -> c15(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), PLUS(x(z0, z1), z0), X(z0, z1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(tt) -> c22(ACTIVE(tt)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c24(ACTIVE(0)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), S(plus(z0, z1)), PLUS(z0, z1)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), PLUS(x(z0, z1), z0), X(z0, z1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(tt) -> c22(ACTIVE(tt)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c24(ACTIVE(0)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, and_2, plus_2, s_1, x_2, encArg_1, encode_active_1, encode_and_2, encode_tt, encode_mark_1, encode_plus_2, encode_0, encode_s_1, encode_x_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2 Compound Symbols: c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_2, c9_3, c11_2, c12_3, c14_2, c15_3, c16_1, c17_1, c18_3, c19_1, c20_3, c21_3, c22_1, c23_4, c24_1, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 encode_s(z0) -> s(encArg(z0)) encode_x(z0, z1) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(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_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c8(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_AND(z0, z1) -> c9(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MARK(z0) -> c11(MARK(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_S(z0) -> c14(S(encArg(z0)), ENCARG(z0)) ENCODE_X(z0, z1) -> c15(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: active_1, mark_1, and_2, plus_2, s_1, x_2, encArg_1, encode_active_1, encode_and_2, encode_tt, encode_mark_1, encode_plus_2, encode_0, encode_s_1, encode_x_2 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2 Compound Symbols: c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c8_2, c9_3, c11_2, c12_3, c14_2, c15_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24 ---------------------------------------- (41) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 encode_s(z0) -> s(encArg(z0)) encode_x(z0, z1) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(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_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(ENCARG(z0)) ENCODE_AND(z0, z1) -> c(ENCARG(z1)) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_PLUS(z0, z1) -> c(ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c(ENCARG(z1)) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_S(z0) -> c(ENCARG(z0)) ENCODE_X(z0, z1) -> c(X(encArg(z0), encArg(z1))) ENCODE_X(z0, z1) -> c(ENCARG(z0)) ENCODE_X(z0, z1) -> c(ENCARG(z1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: active_1, mark_1, and_2, plus_2, s_1, x_2, encArg_1, encode_active_1, encode_and_2, encode_tt, encode_mark_1, encode_plus_2, encode_0, encode_s_1, encode_x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1 ---------------------------------------- (43) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 9 leading nodes: ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_AND(z0, z1) -> c(ENCARG(z0)) ENCODE_AND(z0, z1) -> c(ENCARG(z1)) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c(ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c(ENCARG(z1)) ENCODE_S(z0) -> c(ENCARG(z0)) ENCODE_X(z0, z1) -> c(ENCARG(z0)) ENCODE_X(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) encode_active(z0) -> active(encArg(z0)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 encode_s(z0) -> s(encArg(z0)) encode_x(z0, z1) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(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_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(encArg(z0), encArg(z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: active_1, mark_1, and_2, plus_2, s_1, x_2, encArg_1, encode_active_1, encode_and_2, encode_tt, encode_mark_1, encode_plus_2, encode_0, encode_s_1, encode_x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1 ---------------------------------------- (45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_active(z0) -> active(encArg(z0)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 encode_s(z0) -> s(encArg(z0)) encode_x(z0, z1) -> x(encArg(z0), encArg(z1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(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_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(encArg(z0), encArg(z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c2_2, c3_2, c4_3, c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, 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(tt)) -> c2(ACTIVE(tt), ENCARG(tt)) ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) 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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(encArg(z0), encArg(z1))) ENCARG(cons_active(tt)) -> c2(ACTIVE(tt), ENCARG(tt)) ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) 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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c3_2, c4_3, c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2 ---------------------------------------- (49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(tt)) -> c2(ACTIVE(tt), ENCARG(tt)) ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c3_2, c4_3, c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, 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(tt)) -> c3(MARK(tt), ENCARG(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0), ENCARG(0)) 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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt), ENCARG(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0), ENCARG(0)) 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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c4_3, c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, 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(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c4_3, c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(z0, z1)) -> c4(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c5_3, c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_plus(z0, z1)) -> c5(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c6_2, c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, 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(tt)) -> c6(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(tt)) -> c6(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_s(tt)) -> c6(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c7_3, c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_x(z0, z1)) -> c7(X(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1 Compound Symbols: c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1 Compound Symbols: c16_1, c17_1, c19_1, c21_3, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c21(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) by MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1 Compound Symbols: c16_1, c17_1, c19_1, c23_4, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c23(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1 Compound Symbols: c16_1, c17_1, c19_1, c25_3, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(s(z0)) -> c25(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) by MARK(s(z0)) -> c25(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(z0)) -> c25(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(z0)) -> c25(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1 Compound Symbols: c16_1, c17_1, c19_1, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, MARK_1, AND_2, PLUS_2, S_1, X_2, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1 Compound Symbols: c16_1, c17_1, c19_1, c26_4, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(x(z0, z1)) -> c26(ACTIVE(x(mark(z0), mark(z1))), X(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) by ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) by ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_MARK(z0) -> c(MARK(encArg(z0))) by ENCODE_MARK(tt) -> c(MARK(tt)) ENCODE_MARK(0) -> c(MARK(0)) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(tt) -> c(MARK(tt)) ENCODE_MARK(0) -> c(MARK(0)) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (89) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_MARK(tt) -> c(MARK(tt)) ENCODE_MARK(0) -> c(MARK(0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) by ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_S_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_S(z0) -> c(S(encArg(z0))) by ENCODE_S(tt) -> c(S(tt)) ENCODE_S(0) -> c(S(0)) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_S(tt) -> c(S(tt)) ENCODE_S(0) -> c(S(0)) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_S(0) -> c(S(0)) ENCODE_S(tt) -> c(S(tt)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCODE_X(z0, z1) -> c(X(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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCODE_X_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_X(z0, z1) -> c(X(encArg(z0), encArg(z1))) by ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 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_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1 ---------------------------------------- (99) 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(tt))) -> c2(ACTIVE(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) 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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) 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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1 ---------------------------------------- (103) 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(tt))) -> c2(ACTIVE(mark(tt)), ENCARG(cons_mark(tt))) ENCARG(cons_active(cons_mark(0))) -> c2(ACTIVE(mark(0)), ENCARG(cons_mark(0))) 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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c2(ACTIVE(mark(tt)), ENCARG(cons_mark(tt))) ENCARG(cons_active(cons_mark(0))) -> c2(ACTIVE(mark(0)), ENCARG(cons_mark(0))) 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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1 ---------------------------------------- (105) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) ENCARG(cons_active(cons_mark(0))) -> c1(ACTIVE(mark(0))) ENCARG(cons_active(cons_mark(0))) -> c1(ENCARG(cons_mark(0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c1_1 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) by ENCARG(cons_active(cons_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c1_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) by ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(z0, z1), x1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(z0, z1), x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c1_1 ---------------------------------------- (111) 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(tt))) -> c2(ACTIVE(s(tt)), ENCARG(cons_s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) 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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt)), ENCARG(cons_s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) 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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c1_1 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_s(tt))) -> c2(ACTIVE(s(tt)), ENCARG(cons_s(tt))) ENCARG(cons_active(cons_s(0))) -> c2(ACTIVE(s(0)), ENCARG(cons_s(0))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c2_2, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c1_1 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_x(z0, z1))) -> c2(ACTIVE(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) by ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(z0, z1), x1))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 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_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(z0, z1), x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1 ---------------------------------------- (117) 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(tt))) -> c3(MARK(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) 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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(z0, z1), x1))) ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) 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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_mark(cons_active(tt))) -> c3(MARK(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_mark(cons_active(0))) -> c3(MARK(active(0)), ENCARG(cons_active(0))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1 ---------------------------------------- (121) 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(tt))) -> c3(MARK(mark(tt)), ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c3(MARK(mark(0)), ENCARG(cons_mark(0))) 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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c3(MARK(mark(tt)), ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c3(MARK(mark(0)), ENCARG(cons_mark(0))) 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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1 ---------------------------------------- (123) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(x0, cons_and(z0, z1))) -> c4(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) by ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c4(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) by ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(x0, cons_s(z0))) -> c4(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) by ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0), ENCARG(cons_s(tt))) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0), ENCARG(cons_s(0))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(tt), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(0), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0), ENCARG(cons_s(tt))) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0), ENCARG(cons_s(0))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(tt), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(0), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(x0, cons_x(z0, z1))) -> c4(AND(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) by ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(cons_and(z0, z1), x1)) -> c4(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) by ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1)), ENCARG(tt)) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1)), ENCARG(0)) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_and(z0, z1))) -> c4(AND(and(encArg(x0), encArg(x1)), and(encArg(z0), encArg(z1))), ENCARG(cons_and(x0, x1)), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(cons_and(x0, x1), cons_plus(z0, z1))) -> c4(AND(and(encArg(x0), encArg(x1)), plus(encArg(z0), encArg(z1))), ENCARG(cons_and(x0, x1)), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(cons_and(x0, x1), cons_s(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), s(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_s(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_x(z0, z1))) -> c4(AND(and(encArg(x0), encArg(x1)), x(encArg(z0), encArg(z1))), ENCARG(cons_and(x0, x1)), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1)), ENCARG(tt)) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1)), ENCARG(0)) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c4(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) by ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1)), ENCARG(tt)) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1)), ENCARG(0)) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_and(z0, z1))) -> c4(AND(plus(encArg(x0), encArg(x1)), and(encArg(z0), encArg(z1))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(cons_plus(x0, x1), cons_plus(z0, z1))) -> c4(AND(plus(encArg(x0), encArg(x1)), plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(cons_plus(x0, x1), cons_s(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), s(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_s(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_x(z0, z1))) -> c4(AND(plus(encArg(x0), encArg(x1)), x(encArg(z0), encArg(z1))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1)), ENCARG(tt)) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1)), ENCARG(0)) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(cons_s(z0), x1)) -> c4(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) by ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0)), ENCARG(tt)) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0)), ENCARG(0)) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(x0), cons_and(z0, z1))) -> c4(AND(s(encArg(x0)), and(encArg(z0), encArg(z1))), ENCARG(cons_s(x0)), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(cons_s(x0), cons_plus(z0, z1))) -> c4(AND(s(encArg(x0)), plus(encArg(z0), encArg(z1))), ENCARG(cons_s(x0)), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(cons_s(x0), cons_s(z0))) -> c4(AND(s(encArg(x0)), s(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_s(z0))) ENCARG(cons_and(cons_s(x0), cons_x(z0, z1))) -> c4(AND(s(encArg(x0)), x(encArg(z0), encArg(z1))), ENCARG(cons_s(x0)), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(cons_s(tt)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(cons_s(0)), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0)), ENCARG(tt)) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0)), ENCARG(0)) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(cons_s(tt)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(cons_s(0)), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(cons_x(z0, z1), x1)) -> c4(AND(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) by ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1)), ENCARG(tt)) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1)), ENCARG(0)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_and(z0, z1))) -> c4(AND(x(encArg(x0), encArg(x1)), and(encArg(z0), encArg(z1))), ENCARG(cons_x(x0, x1)), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(cons_x(x0, x1), cons_plus(z0, z1))) -> c4(AND(x(encArg(x0), encArg(x1)), plus(encArg(z0), encArg(z1))), ENCARG(cons_x(x0, x1)), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(cons_x(x0, x1), cons_s(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), s(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_s(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_x(z0, z1))) -> c4(AND(x(encArg(x0), encArg(x1)), x(encArg(z0), encArg(z1))), ENCARG(cons_x(x0, x1)), ENCARG(cons_x(z0, z1))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1)), ENCARG(tt)) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1)), ENCARG(0)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(x0, tt)) -> c4(AND(encArg(x0), tt), ENCARG(x0)) by ENCARG(cons_and(tt, tt)) -> c4(AND(tt, tt), ENCARG(tt)) ENCARG(cons_and(0, tt)) -> c4(AND(0, tt), ENCARG(0)) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(z0, z1), tt)) -> c4(AND(and(encArg(z0), encArg(z1)), tt), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(cons_plus(z0, z1), tt)) -> c4(AND(plus(encArg(z0), encArg(z1)), tt), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(cons_s(z0), tt)) -> c4(AND(s(encArg(z0)), tt), ENCARG(cons_s(z0))) ENCARG(cons_and(cons_x(z0, z1), tt)) -> c4(AND(x(encArg(z0), encArg(z1)), tt), ENCARG(cons_x(z0, z1))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(tt, tt)) -> c4(AND(tt, tt), ENCARG(tt)) ENCARG(cons_and(0, tt)) -> c4(AND(0, tt), ENCARG(0)) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (159) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_and(0, tt)) -> c4(AND(0, tt), ENCARG(0)) ENCARG(cons_and(tt, tt)) -> c4(AND(tt, tt), ENCARG(tt)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(x0, 0)) -> c4(AND(encArg(x0), 0), ENCARG(x0)) by ENCARG(cons_and(tt, 0)) -> c4(AND(tt, 0), ENCARG(tt)) ENCARG(cons_and(0, 0)) -> c4(AND(0, 0), ENCARG(0)) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(z0, z1), 0)) -> c4(AND(and(encArg(z0), encArg(z1)), 0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(cons_plus(z0, z1), 0)) -> c4(AND(plus(encArg(z0), encArg(z1)), 0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(cons_s(z0), 0)) -> c4(AND(s(encArg(z0)), 0), ENCARG(cons_s(z0))) ENCARG(cons_and(cons_x(z0, z1), 0)) -> c4(AND(x(encArg(z0), encArg(z1)), 0), ENCARG(cons_x(z0, z1))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, 0)) -> c4(AND(tt, 0), ENCARG(tt)) ENCARG(cons_and(0, 0)) -> c4(AND(0, 0), ENCARG(0)) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (163) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_and(tt, 0)) -> c4(AND(tt, 0), ENCARG(tt)) ENCARG(cons_and(0, 0)) -> c4(AND(0, 0), ENCARG(0)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(tt, x1)) -> c4(AND(tt, encArg(x1)), ENCARG(x1)) by ENCARG(cons_and(tt, tt)) -> c4(AND(tt, tt), ENCARG(tt)) ENCARG(cons_and(tt, 0)) -> c4(AND(tt, 0), ENCARG(0)) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_and(z0, z1))) -> c4(AND(tt, and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(tt, cons_plus(z0, z1))) -> c4(AND(tt, plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(tt, cons_s(z0))) -> c4(AND(tt, s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_and(tt, cons_x(z0, z1))) -> c4(AND(tt, x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, tt)) -> c4(AND(tt, tt), ENCARG(tt)) ENCARG(cons_and(tt, 0)) -> c4(AND(tt, 0), ENCARG(0)) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (167) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_and(tt, 0)) -> c4(AND(tt, 0), ENCARG(0)) ENCARG(cons_and(tt, tt)) -> c4(AND(tt, tt), ENCARG(tt)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c4_2, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(0, x1)) -> c4(AND(0, encArg(x1)), ENCARG(x1)) by ENCARG(cons_and(0, tt)) -> c4(AND(0, tt), ENCARG(tt)) ENCARG(cons_and(0, 0)) -> c4(AND(0, 0), ENCARG(0)) ENCARG(cons_and(0, cons_active(z0))) -> c4(AND(0, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(0, cons_mark(z0))) -> c4(AND(0, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(0, cons_and(z0, z1))) -> c4(AND(0, and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(0, cons_plus(z0, z1))) -> c4(AND(0, plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(0, cons_s(z0))) -> c4(AND(0, s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_and(0, cons_x(z0, z1))) -> c4(AND(0, x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(0, tt)) -> c4(AND(0, tt), ENCARG(tt)) ENCARG(cons_and(0, 0)) -> c4(AND(0, 0), ENCARG(0)) ENCARG(cons_and(0, cons_active(z0))) -> c4(AND(0, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(0, cons_mark(z0))) -> c4(AND(0, mark(encArg(z0))), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1, c4_2 ---------------------------------------- (171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_and(0, tt)) -> c4(AND(0, tt), ENCARG(tt)) ENCARG(cons_and(0, 0)) -> c4(AND(0, 0), ENCARG(0)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(0, cons_active(z0))) -> c4(AND(0, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(0, cons_mark(z0))) -> c4(AND(0, mark(encArg(z0))), ENCARG(cons_mark(z0))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1, c4_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c5(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) by ENCARG(cons_plus(x0, cons_and(x1, tt))) -> c5(PLUS(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_plus(x0, cons_and(x1, 0))) -> c5(PLUS(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_plus(x0, cons_and(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_and(tt, x2))) -> c5(PLUS(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_plus(x0, cons_and(0, x2))) -> c5(PLUS(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_plus(x0, cons_and(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_plus(tt, cons_and(x1, x2))) -> c5(PLUS(tt, and(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(0, cons_and(x1, x2))) -> c5(PLUS(0, and(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_active(z0), cons_and(x1, x2))) -> c5(PLUS(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_and(x1, x2))) -> c5(PLUS(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_and(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_and(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_and(x1, x2))) -> c5(PLUS(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_and(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(0, cons_active(z0))) -> c4(AND(0, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(0, cons_mark(z0))) -> c4(AND(0, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(x1, tt))) -> c5(PLUS(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_plus(x0, cons_and(x1, 0))) -> c5(PLUS(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_plus(x0, cons_and(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_and(tt, x2))) -> c5(PLUS(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_plus(x0, cons_and(0, x2))) -> c5(PLUS(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_plus(x0, cons_and(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_plus(tt, cons_and(x1, x2))) -> c5(PLUS(tt, and(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(0, cons_and(x1, x2))) -> c5(PLUS(0, and(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_active(z0), cons_and(x1, x2))) -> c5(PLUS(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_and(x1, x2))) -> c5(PLUS(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_and(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_and(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_and(x1, x2))) -> c5(PLUS(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_and(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1, c4_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(0, cons_active(z0))) -> c4(AND(0, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(0, cons_mark(z0))) -> c4(AND(0, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(x1, tt))) -> c5(PLUS(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_plus(x0, cons_and(x1, 0))) -> c5(PLUS(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_plus(x0, cons_and(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_and(tt, x2))) -> c5(PLUS(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_plus(x0, cons_and(0, x2))) -> c5(PLUS(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_plus(x0, cons_and(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_plus(cons_active(z0), cons_and(x1, x2))) -> c5(PLUS(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_and(x1, x2))) -> c5(PLUS(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_and(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_and(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_and(x1, x2))) -> c5(PLUS(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_and(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(tt, cons_and(x1, x2))) -> c5(PLUS(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(0, cons_and(x1, x2))) -> c5(PLUS(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1, c4_2 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c5(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) by ENCARG(cons_plus(x0, cons_plus(x1, tt))) -> c5(PLUS(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_plus(x0, cons_plus(x1, 0))) -> c5(PLUS(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_plus(x0, cons_plus(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(tt, x2))) -> c5(PLUS(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_plus(x0, cons_plus(0, x2))) -> c5(PLUS(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_plus(x0, cons_plus(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_plus(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_plus(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_plus(tt, cons_plus(x1, x2))) -> c5(PLUS(tt, plus(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(0, cons_plus(x1, x2))) -> c5(PLUS(0, plus(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_active(z0), cons_plus(x1, x2))) -> c5(PLUS(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_plus(x1, x2))) -> c5(PLUS(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_plus(x1, x2))) -> c5(PLUS(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(0, cons_active(z0))) -> c4(AND(0, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(0, cons_mark(z0))) -> c4(AND(0, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(x1, tt))) -> c5(PLUS(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_plus(x0, cons_and(x1, 0))) -> c5(PLUS(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_plus(x0, cons_and(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_and(tt, x2))) -> c5(PLUS(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_plus(x0, cons_and(0, x2))) -> c5(PLUS(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_plus(x0, cons_and(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_plus(cons_active(z0), cons_and(x1, x2))) -> c5(PLUS(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_and(x1, x2))) -> c5(PLUS(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_and(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_and(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_and(x1, x2))) -> c5(PLUS(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_and(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(tt, cons_and(x1, x2))) -> c5(PLUS(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(0, cons_and(x1, x2))) -> c5(PLUS(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(x0, cons_plus(x1, tt))) -> c5(PLUS(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_plus(x0, cons_plus(x1, 0))) -> c5(PLUS(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_plus(x0, cons_plus(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(tt, x2))) -> c5(PLUS(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_plus(x0, cons_plus(0, x2))) -> c5(PLUS(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_plus(x0, cons_plus(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_plus(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_plus(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_plus(tt, cons_plus(x1, x2))) -> c5(PLUS(tt, plus(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(0, cons_plus(x1, x2))) -> c5(PLUS(0, plus(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_active(z0), cons_plus(x1, x2))) -> c5(PLUS(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_plus(x1, x2))) -> c5(PLUS(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_plus(x1, x2))) -> c5(PLUS(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1, c4_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_x(z0, z1)) -> x(encArg(z0), encArg(z1)) active(and(tt, z0)) -> mark(z0) active(plus(z0, 0)) -> mark(z0) active(plus(z0, s(z1))) -> mark(s(plus(z0, z1))) active(x(z0, 0)) -> mark(0) active(x(z0, s(z1))) -> mark(plus(x(z0, z1), z0)) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(tt) -> active(tt) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(0) -> active(0) mark(s(z0)) -> active(s(mark(z0))) mark(x(z0, z1)) -> active(x(mark(z0), mark(z1))) and(mark(z0), z1) -> and(z0, z1) and(z0, mark(z1)) -> and(z0, z1) and(active(z0), z1) -> and(z0, z1) and(z0, active(z1)) -> and(z0, z1) plus(mark(z0), z1) -> plus(z0, z1) plus(z0, mark(z1)) -> plus(z0, z1) plus(active(z0), z1) -> plus(z0, z1) plus(z0, active(z1)) -> plus(z0, z1) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) x(mark(z0), z1) -> x(z0, z1) x(z0, mark(z1)) -> x(z0, z1) x(active(z0), z1) -> x(z0, z1) x(z0, active(z1)) -> x(z0, z1) Tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_x(z0, z1))) -> c3(MARK(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c4(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c4(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c4(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c4(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, cons_active(z0))) -> c5(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c5(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_s(z0))) -> c5(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_x(z0, z1))) -> c5(PLUS(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c5(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c5(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c5(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c5(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c5(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_x(z0, z1), x1)) -> c5(PLUS(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c5(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c5(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c5(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c5(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_s(cons_active(z0))) -> c6(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c6(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_x(z0, z1))) -> c6(S(x(encArg(z0), encArg(z1))), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(x0, cons_active(z0))) -> c7(X(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_x(x0, cons_mark(z0))) -> c7(X(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_x(x0, cons_and(z0, z1))) -> c7(X(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_x(x0, cons_plus(z0, z1))) -> c7(X(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_x(x0, cons_s(z0))) -> c7(X(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_x(x0, cons_x(z0, z1))) -> c7(X(encArg(x0), x(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_x(z0, z1))) ENCARG(cons_x(cons_active(z0), x1)) -> c7(X(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_x(cons_mark(z0), x1)) -> c7(X(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_x(cons_and(z0, z1), x1)) -> c7(X(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_plus(z0, z1), x1)) -> c7(X(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_x(cons_s(z0), x1)) -> c7(X(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_x(cons_x(z0, z1), x1)) -> c7(X(x(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_x(z0, z1)), ENCARG(x1)) ENCARG(cons_x(x0, tt)) -> c7(X(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_x(x0, 0)) -> c7(X(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_x(tt, x1)) -> c7(X(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_x(0, x1)) -> c7(X(0, encArg(x1)), ENCARG(x1)) MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(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_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_x(z0, z1)) -> c(ACTIVE(x(encArg(z0), encArg(z1)))) ENCODE_AND(x0, tt) -> c(AND(encArg(x0), tt)) ENCODE_AND(x0, 0) -> c(AND(encArg(x0), 0)) ENCODE_AND(x0, cons_active(z0)) -> c(AND(encArg(x0), active(encArg(z0)))) ENCODE_AND(x0, cons_mark(z0)) -> c(AND(encArg(x0), mark(encArg(z0)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_x(z0, z1)) -> c(AND(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_AND(tt, x1) -> c(AND(tt, encArg(x1))) ENCODE_AND(0, x1) -> c(AND(0, encArg(x1))) ENCODE_AND(cons_active(z0), x1) -> c(AND(active(encArg(z0)), encArg(x1))) ENCODE_AND(cons_mark(z0), x1) -> c(AND(mark(encArg(z0)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_x(z0, z1), x1) -> c(AND(x(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_MARK(cons_active(z0)) -> c(MARK(active(encArg(z0)))) ENCODE_MARK(cons_mark(z0)) -> c(MARK(mark(encArg(z0)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_x(z0, z1)) -> c(MARK(x(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, tt) -> c(PLUS(encArg(x0), tt)) ENCODE_PLUS(x0, 0) -> c(PLUS(encArg(x0), 0)) ENCODE_PLUS(x0, cons_active(z0)) -> c(PLUS(encArg(x0), active(encArg(z0)))) ENCODE_PLUS(x0, cons_mark(z0)) -> c(PLUS(encArg(x0), mark(encArg(z0)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_x(z0, z1)) -> c(PLUS(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_PLUS(tt, x1) -> c(PLUS(tt, encArg(x1))) ENCODE_PLUS(0, x1) -> c(PLUS(0, encArg(x1))) ENCODE_PLUS(cons_active(z0), x1) -> c(PLUS(active(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_mark(z0), x1) -> c(PLUS(mark(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_x(z0, z1), x1) -> c(PLUS(x(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_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_x(z0, z1)) -> c(S(x(encArg(z0), encArg(z1)))) ENCODE_X(x0, tt) -> c(X(encArg(x0), tt)) ENCODE_X(x0, 0) -> c(X(encArg(x0), 0)) ENCODE_X(x0, cons_active(z0)) -> c(X(encArg(x0), active(encArg(z0)))) ENCODE_X(x0, cons_mark(z0)) -> c(X(encArg(x0), mark(encArg(z0)))) ENCODE_X(x0, cons_and(z0, z1)) -> c(X(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_plus(z0, z1)) -> c(X(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_X(x0, cons_s(z0)) -> c(X(encArg(x0), s(encArg(z0)))) ENCODE_X(x0, cons_x(z0, z1)) -> c(X(encArg(x0), x(encArg(z0), encArg(z1)))) ENCODE_X(tt, x1) -> c(X(tt, encArg(x1))) ENCODE_X(0, x1) -> c(X(0, encArg(x1))) ENCODE_X(cons_active(z0), x1) -> c(X(active(encArg(z0)), encArg(x1))) ENCODE_X(cons_mark(z0), x1) -> c(X(mark(encArg(z0)), encArg(x1))) ENCODE_X(cons_and(z0, z1), x1) -> c(X(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_plus(z0, z1), x1) -> c(X(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_X(cons_s(z0), x1) -> c(X(s(encArg(z0)), encArg(x1))) ENCODE_X(cons_x(z0, z1), x1) -> c(X(x(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_and(z0, z1)))) -> c2(ACTIVE(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_active(cons_active(cons_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_active(cons_mark(cons_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_active(cons_mark(tt))) -> c1(ACTIVE(mark(tt))) ENCARG(cons_active(cons_mark(tt))) -> c1(ENCARG(cons_mark(tt))) 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_and(x0, tt))) -> c2(ACTIVE(and(encArg(x0), tt)), ENCARG(cons_and(x0, tt))) ENCARG(cons_active(cons_and(x0, 0))) -> c2(ACTIVE(and(encArg(x0), 0)), ENCARG(cons_and(x0, 0))) ENCARG(cons_active(cons_and(x0, cons_active(z0)))) -> c2(ACTIVE(and(encArg(x0), active(encArg(z0)))), ENCARG(cons_and(x0, cons_active(z0)))) ENCARG(cons_active(cons_and(x0, cons_mark(z0)))) -> c2(ACTIVE(and(encArg(x0), mark(encArg(z0)))), ENCARG(cons_and(x0, cons_mark(z0)))) ENCARG(cons_active(cons_and(x0, cons_and(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_s(z0)))) -> c2(ACTIVE(and(encArg(x0), s(encArg(z0)))), ENCARG(cons_and(x0, cons_s(z0)))) ENCARG(cons_active(cons_and(x0, cons_x(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_and(tt, x1))) -> c2(ACTIVE(and(tt, encArg(x1))), ENCARG(cons_and(tt, x1))) ENCARG(cons_active(cons_and(0, x1))) -> c2(ACTIVE(and(0, encArg(x1))), ENCARG(cons_and(0, x1))) ENCARG(cons_active(cons_and(cons_active(z0), x1))) -> c2(ACTIVE(and(active(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_active(z0), x1))) ENCARG(cons_active(cons_and(cons_mark(z0), x1))) -> c2(ACTIVE(and(mark(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_mark(z0), x1))) ENCARG(cons_active(cons_and(cons_and(z0, z1), x1))) -> c2(ACTIVE(and(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_plus(z0, z1), x1))) -> c2(ACTIVE(and(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_s(z0), x1))) -> c2(ACTIVE(and(s(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_s(z0), x1))) ENCARG(cons_active(cons_and(cons_x(z0, z1), x1))) -> c2(ACTIVE(and(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_x(z0, z1), x1))) ENCARG(cons_active(cons_plus(x0, tt))) -> c2(ACTIVE(plus(encArg(x0), tt)), ENCARG(cons_plus(x0, tt))) ENCARG(cons_active(cons_plus(x0, 0))) -> c2(ACTIVE(plus(encArg(x0), 0)), ENCARG(cons_plus(x0, 0))) ENCARG(cons_active(cons_plus(x0, cons_active(z0)))) -> c2(ACTIVE(plus(encArg(x0), active(encArg(z0)))), ENCARG(cons_plus(x0, cons_active(z0)))) ENCARG(cons_active(cons_plus(x0, cons_mark(z0)))) -> c2(ACTIVE(plus(encArg(x0), mark(encArg(z0)))), ENCARG(cons_plus(x0, cons_mark(z0)))) ENCARG(cons_active(cons_plus(x0, cons_and(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_s(z0)))) -> c2(ACTIVE(plus(encArg(x0), s(encArg(z0)))), ENCARG(cons_plus(x0, cons_s(z0)))) ENCARG(cons_active(cons_plus(x0, cons_x(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_plus(tt, x1))) -> c2(ACTIVE(plus(tt, encArg(x1))), ENCARG(cons_plus(tt, x1))) ENCARG(cons_active(cons_plus(0, x1))) -> c2(ACTIVE(plus(0, encArg(x1))), ENCARG(cons_plus(0, x1))) ENCARG(cons_active(cons_plus(cons_active(z0), x1))) -> c2(ACTIVE(plus(active(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_active(z0), x1))) ENCARG(cons_active(cons_plus(cons_mark(z0), x1))) -> c2(ACTIVE(plus(mark(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_mark(z0), x1))) ENCARG(cons_active(cons_plus(cons_and(z0, z1), x1))) -> c2(ACTIVE(plus(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_plus(z0, z1), x1))) -> c2(ACTIVE(plus(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_s(z0), x1))) -> c2(ACTIVE(plus(s(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_s(z0), x1))) ENCARG(cons_active(cons_plus(cons_x(z0, z1), x1))) -> c2(ACTIVE(plus(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_x(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_and(z0, z1)))) -> c2(ACTIVE(s(and(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_active(cons_s(cons_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(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_x(z0, z1)))) -> c2(ACTIVE(s(x(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_active(cons_x(x0, tt))) -> c2(ACTIVE(x(encArg(x0), tt)), ENCARG(cons_x(x0, tt))) ENCARG(cons_active(cons_x(x0, 0))) -> c2(ACTIVE(x(encArg(x0), 0)), ENCARG(cons_x(x0, 0))) ENCARG(cons_active(cons_x(x0, cons_active(z0)))) -> c2(ACTIVE(x(encArg(x0), active(encArg(z0)))), ENCARG(cons_x(x0, cons_active(z0)))) ENCARG(cons_active(cons_x(x0, cons_mark(z0)))) -> c2(ACTIVE(x(encArg(x0), mark(encArg(z0)))), ENCARG(cons_x(x0, cons_mark(z0)))) ENCARG(cons_active(cons_x(x0, cons_and(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_x(x0, cons_s(z0)))) -> c2(ACTIVE(x(encArg(x0), s(encArg(z0)))), ENCARG(cons_x(x0, cons_s(z0)))) ENCARG(cons_active(cons_x(x0, cons_x(z0, z1)))) -> c2(ACTIVE(x(encArg(x0), x(encArg(z0), encArg(z1)))), ENCARG(cons_x(x0, cons_x(z0, z1)))) ENCARG(cons_active(cons_x(tt, x1))) -> c2(ACTIVE(x(tt, encArg(x1))), ENCARG(cons_x(tt, x1))) ENCARG(cons_active(cons_x(0, x1))) -> c2(ACTIVE(x(0, encArg(x1))), ENCARG(cons_x(0, x1))) ENCARG(cons_active(cons_x(cons_active(z0), x1))) -> c2(ACTIVE(x(active(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_active(z0), x1))) ENCARG(cons_active(cons_x(cons_mark(z0), x1))) -> c2(ACTIVE(x(mark(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_mark(z0), x1))) ENCARG(cons_active(cons_x(cons_and(z0, z1), x1))) -> c2(ACTIVE(x(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_plus(z0, z1), x1))) -> c2(ACTIVE(x(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_x(cons_s(z0), x1))) -> c2(ACTIVE(x(s(encArg(z0)), encArg(x1))), ENCARG(cons_x(cons_s(z0), x1))) ENCARG(cons_active(cons_x(cons_x(z0, z1), x1))) -> c2(ACTIVE(x(x(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_x(cons_x(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_and(z0, z1)))) -> c3(MARK(active(and(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_and(z0, z1)))) ENCARG(cons_mark(cons_active(cons_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(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_x(z0, z1)))) -> c3(MARK(active(x(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_x(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_and(z0, z1)))) -> c3(MARK(mark(and(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_and(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(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_x(z0, z1)))) -> c3(MARK(mark(x(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_x(z0, z1)))) ENCARG(cons_mark(cons_mark(tt))) -> c8(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c8(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c8(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c8(ENCARG(cons_mark(0))) ENCARG(cons_and(x0, cons_and(x1, tt))) -> c4(AND(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_and(x0, cons_and(x1, 0))) -> c4(AND(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_and(x0, cons_and(x1, cons_active(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_and(x1, cons_s(z0)))) -> c4(AND(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_and(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_and(tt, x2))) -> c4(AND(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_and(x0, cons_and(0, x2))) -> c4(AND(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_and(x0, cons_and(cons_active(z0), x2))) -> c4(AND(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_mark(z0), x2))) -> c4(AND(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_and(cons_s(z0), x2))) -> c4(AND(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_and(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_and(x1, x2))) -> c4(AND(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_and(x1, x2))) -> c4(AND(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_and(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_and(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_and(x1, x2))) -> c4(AND(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_and(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(tt, cons_and(x1, x2))) -> c4(AND(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(0, cons_and(x1, x2))) -> c4(AND(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_and(x0, cons_plus(x1, tt))) -> c4(AND(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_and(x0, cons_plus(x1, 0))) -> c4(AND(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_and(x0, cons_plus(x1, cons_active(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_plus(x1, cons_s(z0)))) -> c4(AND(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_plus(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_plus(tt, x2))) -> c4(AND(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_and(x0, cons_plus(0, x2))) -> c4(AND(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_and(x0, cons_plus(cons_active(z0), x2))) -> c4(AND(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_mark(z0), x2))) -> c4(AND(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_plus(cons_s(z0), x2))) -> c4(AND(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_plus(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_plus(x1, x2))) -> c4(AND(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_plus(x1, x2))) -> c4(AND(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_plus(x1, x2))) -> c4(AND(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_plus(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(tt, cons_plus(x1, x2))) -> c4(AND(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(0, cons_plus(x1, x2))) -> c4(AND(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_and(x0, cons_s(cons_active(z0)))) -> c4(AND(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_and(x0, cons_s(cons_mark(z0)))) -> c4(AND(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_and(x0, cons_s(cons_and(z0, z1)))) -> c4(AND(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_plus(z0, z1)))) -> c4(AND(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_s(cons_s(z0)))) -> c4(AND(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_and(x0, cons_s(cons_x(z0, z1)))) -> c4(AND(encArg(x0), s(x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_x(z0, z1)))) ENCARG(cons_and(cons_active(z0), cons_s(x1))) -> c4(AND(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_mark(z0), cons_s(x1))) -> c4(AND(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_and(z0, z1), cons_s(x1))) -> c4(AND(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_plus(z0, z1), cons_s(x1))) -> c4(AND(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_s(z0), cons_s(x1))) -> c4(AND(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_and(cons_x(z0, z1), cons_s(x1))) -> c4(AND(x(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_x(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_s(tt))) -> c4(AND(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_and(x0, cons_s(0))) -> c4(AND(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_and(tt, cons_s(x1))) -> c4(AND(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(0, cons_s(x1))) -> c4(AND(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_and(x0, cons_x(x1, tt))) -> c4(AND(encArg(x0), x(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_x(x1, tt))) ENCARG(cons_and(x0, cons_x(x1, 0))) -> c4(AND(encArg(x0), x(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_x(x1, 0))) ENCARG(cons_and(x0, cons_x(x1, cons_active(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_active(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_mark(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_mark(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_and(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_and(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_plus(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_plus(z0, z1)))) ENCARG(cons_and(x0, cons_x(x1, cons_s(z0)))) -> c4(AND(encArg(x0), x(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_x(x1, cons_s(z0)))) ENCARG(cons_and(x0, cons_x(x1, cons_x(z0, z1)))) -> c4(AND(encArg(x0), x(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_x(x1, cons_x(z0, z1)))) ENCARG(cons_and(x0, cons_x(tt, x2))) -> c4(AND(encArg(x0), x(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_x(tt, x2))) ENCARG(cons_and(x0, cons_x(0, x2))) -> c4(AND(encArg(x0), x(0, encArg(x2))), ENCARG(x0), ENCARG(cons_x(0, x2))) ENCARG(cons_and(x0, cons_x(cons_active(z0), x2))) -> c4(AND(encArg(x0), x(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_active(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_mark(z0), x2))) -> c4(AND(encArg(x0), x(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_mark(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_and(z0, z1), x2))) -> c4(AND(encArg(x0), x(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_and(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_plus(z0, z1), x2))) -> c4(AND(encArg(x0), x(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_plus(z0, z1), x2))) ENCARG(cons_and(x0, cons_x(cons_s(z0), x2))) -> c4(AND(encArg(x0), x(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_s(z0), x2))) ENCARG(cons_and(x0, cons_x(cons_x(z0, z1), x2))) -> c4(AND(encArg(x0), x(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_x(cons_x(z0, z1), x2))) ENCARG(cons_and(cons_active(z0), cons_x(x1, x2))) -> c4(AND(active(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_mark(z0), cons_x(x1, x2))) -> c4(AND(mark(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(z0, z1), cons_x(x1, x2))) -> c4(AND(and(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_plus(z0, z1), cons_x(x1, x2))) -> c4(AND(plus(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_s(z0), cons_x(x1, x2))) -> c4(AND(s(encArg(z0)), x(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_x(z0, z1), cons_x(x1, x2))) -> c4(AND(x(encArg(z0), encArg(z1)), x(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(tt, cons_x(x1, x2))) -> c4(AND(tt, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(0, cons_x(x1, x2))) -> c4(AND(0, x(encArg(x1), encArg(x2))), ENCARG(cons_x(x1, x2))) ENCARG(cons_and(cons_and(x0, x1), cons_active(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_and(x0, x1), cons_mark(z0))) -> c4(AND(and(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_and(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_and(x0, tt), x2)) -> c4(AND(and(encArg(x0), tt), encArg(x2)), ENCARG(cons_and(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, 0), x2)) -> c4(AND(and(encArg(x0), 0), encArg(x2)), ENCARG(cons_and(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_active(z0)), x2)) -> c4(AND(and(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_mark(z0)), x2)) -> c4(AND(and(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_and(z0, z1)), x2)) -> c4(AND(and(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_plus(z0, z1)), x2)) -> c4(AND(and(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_s(z0)), x2)) -> c4(AND(and(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_and(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, cons_x(z0, z1)), x2)) -> c4(AND(and(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_and(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_and(tt, x1), x2)) -> c4(AND(and(tt, encArg(x1)), encArg(x2)), ENCARG(cons_and(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(0, x1), x2)) -> c4(AND(and(0, encArg(x1)), encArg(x2)), ENCARG(cons_and(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_active(z0), x1), x2)) -> c4(AND(and(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_mark(z0), x1), x2)) -> c4(AND(and(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_and(z0, z1), x1), x2)) -> c4(AND(and(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_plus(z0, z1), x1), x2)) -> c4(AND(and(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_s(z0), x1), x2)) -> c4(AND(and(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(cons_x(z0, z1), x1), x2)) -> c4(AND(and(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_and(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_and(x0, x1), tt)) -> c4(AND(and(encArg(x0), encArg(x1)), tt), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_and(x0, x1), 0)) -> c4(AND(and(encArg(x0), encArg(x1)), 0), ENCARG(cons_and(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), cons_active(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_plus(x0, x1), cons_mark(z0))) -> c4(AND(plus(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_plus(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_plus(x0, tt), x2)) -> c4(AND(plus(encArg(x0), tt), encArg(x2)), ENCARG(cons_plus(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, 0), x2)) -> c4(AND(plus(encArg(x0), 0), encArg(x2)), ENCARG(cons_plus(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_active(z0)), x2)) -> c4(AND(plus(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_mark(z0)), x2)) -> c4(AND(plus(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_and(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_plus(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_s(z0)), x2)) -> c4(AND(plus(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_plus(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, cons_x(z0, z1)), x2)) -> c4(AND(plus(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_plus(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_plus(tt, x1), x2)) -> c4(AND(plus(tt, encArg(x1)), encArg(x2)), ENCARG(cons_plus(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(0, x1), x2)) -> c4(AND(plus(0, encArg(x1)), encArg(x2)), ENCARG(cons_plus(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_active(z0), x1), x2)) -> c4(AND(plus(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_mark(z0), x1), x2)) -> c4(AND(plus(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_and(z0, z1), x1), x2)) -> c4(AND(plus(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_plus(z0, z1), x1), x2)) -> c4(AND(plus(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_s(z0), x1), x2)) -> c4(AND(plus(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(cons_x(z0, z1), x1), x2)) -> c4(AND(plus(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_plus(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_plus(x0, x1), tt)) -> c4(AND(plus(encArg(x0), encArg(x1)), tt), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_plus(x0, x1), 0)) -> c4(AND(plus(encArg(x0), encArg(x1)), 0), ENCARG(cons_plus(x0, x1))) ENCARG(cons_and(cons_s(x0), cons_active(z0))) -> c4(AND(s(encArg(x0)), active(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_s(x0), cons_mark(z0))) -> c4(AND(s(encArg(x0)), mark(encArg(z0))), ENCARG(cons_s(x0)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_s(cons_active(z0)), x1)) -> c4(AND(s(active(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_active(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_mark(z0)), x1)) -> c4(AND(s(mark(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_mark(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_and(z0, z1)), x1)) -> c4(AND(s(and(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_and(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_plus(z0, z1)), x1)) -> c4(AND(s(plus(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_plus(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_s(z0)), x1)) -> c4(AND(s(s(encArg(z0))), encArg(x1)), ENCARG(cons_s(cons_s(z0))), ENCARG(x1)) ENCARG(cons_and(cons_s(cons_x(z0, z1)), x1)) -> c4(AND(s(x(encArg(z0), encArg(z1))), encArg(x1)), ENCARG(cons_s(cons_x(z0, z1))), ENCARG(x1)) ENCARG(cons_and(cons_s(x0), tt)) -> c4(AND(s(encArg(x0)), tt), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(x0), 0)) -> c4(AND(s(encArg(x0)), 0), ENCARG(cons_s(x0))) ENCARG(cons_and(cons_s(tt), x1)) -> c4(AND(s(tt), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_s(0), x1)) -> c4(AND(s(0), encArg(x1)), ENCARG(x1)) ENCARG(cons_and(cons_x(x0, x1), cons_active(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), active(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_x(x0, x1), cons_mark(z0))) -> c4(AND(x(encArg(x0), encArg(x1)), mark(encArg(z0))), ENCARG(cons_x(x0, x1)), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_x(x0, tt), x2)) -> c4(AND(x(encArg(x0), tt), encArg(x2)), ENCARG(cons_x(x0, tt)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, 0), x2)) -> c4(AND(x(encArg(x0), 0), encArg(x2)), ENCARG(cons_x(x0, 0)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_active(z0)), x2)) -> c4(AND(x(encArg(x0), active(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_active(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_mark(z0)), x2)) -> c4(AND(x(encArg(x0), mark(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_mark(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_and(z0, z1)), x2)) -> c4(AND(x(encArg(x0), and(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_and(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_plus(z0, z1)), x2)) -> c4(AND(x(encArg(x0), plus(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_plus(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_s(z0)), x2)) -> c4(AND(x(encArg(x0), s(encArg(z0))), encArg(x2)), ENCARG(cons_x(x0, cons_s(z0))), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, cons_x(z0, z1)), x2)) -> c4(AND(x(encArg(x0), x(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_x(x0, cons_x(z0, z1))), ENCARG(x2)) ENCARG(cons_and(cons_x(tt, x1), x2)) -> c4(AND(x(tt, encArg(x1)), encArg(x2)), ENCARG(cons_x(tt, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(0, x1), x2)) -> c4(AND(x(0, encArg(x1)), encArg(x2)), ENCARG(cons_x(0, x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_active(z0), x1), x2)) -> c4(AND(x(active(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_active(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_mark(z0), x1), x2)) -> c4(AND(x(mark(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_mark(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_and(z0, z1), x1), x2)) -> c4(AND(x(and(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_and(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_plus(z0, z1), x1), x2)) -> c4(AND(x(plus(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_plus(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_s(z0), x1), x2)) -> c4(AND(x(s(encArg(z0)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_s(z0), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(cons_x(z0, z1), x1), x2)) -> c4(AND(x(x(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_x(cons_x(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_and(cons_x(x0, x1), tt)) -> c4(AND(x(encArg(x0), encArg(x1)), tt), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_x(x0, x1), 0)) -> c4(AND(x(encArg(x0), encArg(x1)), 0), ENCARG(cons_x(x0, x1))) ENCARG(cons_and(cons_active(z0), tt)) -> c4(AND(active(encArg(z0)), tt), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), tt)) -> c4(AND(mark(encArg(z0)), tt), ENCARG(cons_mark(z0))) ENCARG(cons_and(cons_active(z0), 0)) -> c4(AND(active(encArg(z0)), 0), ENCARG(cons_active(z0))) ENCARG(cons_and(cons_mark(z0), 0)) -> c4(AND(mark(encArg(z0)), 0), ENCARG(cons_mark(z0))) ENCARG(cons_and(tt, cons_active(z0))) -> c4(AND(tt, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(tt, cons_mark(z0))) -> c4(AND(tt, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_and(0, cons_active(z0))) -> c4(AND(0, active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_and(0, cons_mark(z0))) -> c4(AND(0, mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_and(x1, tt))) -> c5(PLUS(encArg(x0), and(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_and(x1, tt))) ENCARG(cons_plus(x0, cons_and(x1, 0))) -> c5(PLUS(encArg(x0), and(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_and(x1, 0))) ENCARG(cons_plus(x0, cons_and(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_and(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), and(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_and(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_and(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), and(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_and(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_and(tt, x2))) -> c5(PLUS(encArg(x0), and(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_and(tt, x2))) ENCARG(cons_plus(x0, cons_and(0, x2))) -> c5(PLUS(encArg(x0), and(0, encArg(x2))), ENCARG(x0), ENCARG(cons_and(0, x2))) ENCARG(cons_plus(x0, cons_and(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), and(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), and(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_and(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), and(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_and(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), and(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_and(cons_x(z0, z1), x2))) ENCARG(cons_plus(cons_active(z0), cons_and(x1, x2))) -> c5(PLUS(active(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_and(x1, x2))) -> c5(PLUS(mark(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_and(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_and(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_and(x1, x2))) -> c5(PLUS(s(encArg(z0)), and(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_and(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), and(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(tt, cons_and(x1, x2))) -> c5(PLUS(tt, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(0, cons_and(x1, x2))) -> c5(PLUS(0, and(encArg(x1), encArg(x2))), ENCARG(cons_and(x1, x2))) ENCARG(cons_plus(x0, cons_plus(x1, tt))) -> c5(PLUS(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_plus(x0, cons_plus(x1, 0))) -> c5(PLUS(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_plus(x0, cons_plus(x1, cons_active(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_mark(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_and(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_s(z0)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_plus(x0, cons_plus(x1, cons_x(z0, z1)))) -> c5(PLUS(encArg(x0), plus(encArg(x1), x(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_x(z0, z1)))) ENCARG(cons_plus(x0, cons_plus(tt, x2))) -> c5(PLUS(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_plus(x0, cons_plus(0, x2))) -> c5(PLUS(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_plus(x0, cons_plus(cons_active(z0), x2))) -> c5(PLUS(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_mark(z0), x2))) -> c5(PLUS(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_and(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_plus(x0, cons_plus(cons_plus(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_plus(x0, cons_plus(cons_s(z0), x2))) -> c5(PLUS(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_plus(x0, cons_plus(cons_x(z0, z1), x2))) -> c5(PLUS(encArg(x0), plus(x(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_x(z0, z1), x2))) ENCARG(cons_plus(cons_active(z0), cons_plus(x1, x2))) -> c5(PLUS(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_mark(z0), cons_plus(x1, x2))) -> c5(PLUS(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_and(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_plus(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_s(z0), cons_plus(x1, x2))) -> c5(PLUS(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(cons_x(z0, z1), cons_plus(x1, x2))) -> c5(PLUS(x(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_x(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(tt, cons_plus(x1, x2))) -> c5(PLUS(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_plus(0, cons_plus(x1, x2))) -> c5(PLUS(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) S tuples: ACTIVE(and(tt, z0)) -> c16(MARK(z0)) ACTIVE(plus(z0, 0)) -> c17(MARK(z0)) ACTIVE(x(z0, 0)) -> c19(MARK(0)) AND(mark(z0), z1) -> c27(AND(z0, z1)) AND(z0, mark(z1)) -> c28(AND(z0, z1)) AND(active(z0), z1) -> c29(AND(z0, z1)) AND(z0, active(z1)) -> c30(AND(z0, z1)) PLUS(mark(z0), z1) -> c31(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c32(PLUS(z0, z1)) PLUS(active(z0), z1) -> c33(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c34(PLUS(z0, z1)) S(mark(z0)) -> c35(S(z0)) S(active(z0)) -> c36(S(z0)) X(mark(z0), z1) -> c37(X(z0, z1)) X(z0, mark(z1)) -> c38(X(z0, z1)) X(active(z0), z1) -> c39(X(z0, z1)) X(z0, active(z1)) -> c40(X(z0, z1)) ACTIVE(plus(z0, s(z1))) -> c18(MARK(s(plus(z0, z1))), PLUS(z0, z1)) ACTIVE(x(z0, s(z1))) -> c20(MARK(plus(x(z0, z1), z0)), X(z0, z1)) MARK(tt) -> c22 MARK(0) -> c24 MARK(and(z0, z1)) -> c21(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(and(z0, z1), x1)) -> c21(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(tt, x1)) -> c21(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(plus(z0, z1), x1)) -> c21(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(0, x1)) -> c21(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(s(z0), x1)) -> c21(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(x(z0, z1), x1)) -> c21(ACTIVE(and(active(x(mark(z0), mark(z1))), x1)), AND(mark(x(z0, z1)), x1), MARK(x(z0, z1))) MARK(and(x0, x1)) -> c21(AND(mark(x0), x1)) MARK(plus(z0, x1)) -> c23(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c23(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, and(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(and(mark(z0), z1)))), PLUS(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(plus(x0, tt)) -> c23(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, plus(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c23(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(x0, s(z0))) -> c23(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, x(z0, z1))) -> c23(ACTIVE(plus(mark(x0), active(x(mark(z0), mark(z1))))), PLUS(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c23(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c23(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c23(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c23(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(plus(s(z0), x1)) -> c23(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c23(ACTIVE(plus(active(x(mark(z0), mark(z1))), mark(x1))), PLUS(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) MARK(s(and(z0, z1))) -> c25(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(tt)) -> c25(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(plus(z0, z1))) -> c25(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c25(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(s(z0))) -> c25(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(x(z0, z1))) -> c25(ACTIVE(s(active(x(mark(z0), mark(z1))))), S(mark(x(z0, z1))), MARK(x(z0, z1))) MARK(s(z0)) -> c25(S(mark(z0)), MARK(z0)) MARK(x(z0, x1)) -> c26(ACTIVE(x(z0, mark(x1))), X(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(x(x0, z1)) -> c26(ACTIVE(x(mark(x0), z1)), X(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(x(x0, and(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(and(mark(z0), z1)))), X(mark(x0), mark(and(z0, z1))), MARK(x0), MARK(and(z0, z1))) MARK(x(x0, tt)) -> c26(ACTIVE(x(mark(x0), active(tt))), X(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(x(x0, plus(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(plus(mark(z0), mark(z1))))), X(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(x(x0, 0)) -> c26(ACTIVE(x(mark(x0), active(0))), X(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(x(x0, s(z0))) -> c26(ACTIVE(x(mark(x0), active(s(mark(z0))))), X(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(x(x0, x(z0, z1))) -> c26(ACTIVE(x(mark(x0), active(x(mark(z0), mark(z1))))), X(mark(x0), mark(x(z0, z1))), MARK(x0), MARK(x(z0, z1))) MARK(x(and(z0, z1), x1)) -> c26(ACTIVE(x(active(and(mark(z0), z1)), mark(x1))), X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(x(tt, x1)) -> c26(ACTIVE(x(active(tt), mark(x1))), X(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c26(ACTIVE(x(active(plus(mark(z0), mark(z1))), mark(x1))), X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(x(0, x1)) -> c26(ACTIVE(x(active(0), mark(x1))), X(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(x(s(z0), x1)) -> c26(ACTIVE(x(active(s(mark(z0))), mark(x1))), X(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c26(ACTIVE(x(active(x(mark(z0), mark(z1))), mark(x1))), X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1)), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, and_2, plus_2, s_1, x_2 Defined Pair Symbols: ACTIVE_1, AND_2, PLUS_2, S_1, X_2, MARK_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_AND_2, ENCODE_MARK_1, ENCODE_PLUS_2, ENCODE_S_1, ENCODE_X_2 Compound Symbols: c16_1, c17_1, c19_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c18_2, c20_2, c22, c24, c3_2, c3_1, c4_3, c5_3, c5_2, c6_2, c7_3, c7_2, c21_3, c21_1, c23_4, c25_3, c25_2, c26_4, c_1, c2_2, c1_1, c8_1, c4_2