/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 350 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 8979 ms] (12) BOUNDS(1, INF) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) NarrowingProof [BOTH BOUNDS(ID, ID), 8990 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 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), 38 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), 12 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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), 36 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtLeafRemovalProof [ComplexityIfPolyImplication, 7 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtLeafRemovalProof [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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 6 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (120) CdtProblem (121) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (146) CdtProblem (147) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 26 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 157 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 286 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 97 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 248 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (164) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0) -> active(0) U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0 ---------------------------------------- (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(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0) -> active(0) U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0 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(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0) -> active(0) U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0')) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0')) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0') -> active(0') U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0' Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Innermost TRS: Rules: active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0')) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0')) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0') -> active(0') U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0' Types: active :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat s :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat and :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat 0' :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encArg :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_and :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_and :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_0 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat hole_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat1_4 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4 :: Nat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat ---------------------------------------- (9) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: active, mark, s, plus, and, isNat, U11, U21, encArg They will be analysed ascendingly in the following order: active = mark s < active plus < active and < active isNat < active U11 < active U21 < active active < encArg s < mark plus < mark and < mark isNat < mark U11 < mark U21 < mark mark < encArg s < encArg plus < encArg and < encArg isNat < encArg U11 < encArg U21 < encArg ---------------------------------------- (10) Obligation: Innermost TRS: Rules: active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0')) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0')) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0') -> active(0') U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0' Types: active :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat s :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat and :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat 0' :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encArg :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_and :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_and :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_0 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat hole_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat1_4 :: tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4 :: Nat -> tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat Generator Equations: gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4(0) <=> tt gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4(+(x, 1)) <=> cons_active(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4(x)) The following defined symbols remain to be analysed: s, active, mark, plus, and, isNat, U11, U21, encArg They will be analysed ascendingly in the following order: active = mark s < active plus < active and < active isNat < active U11 < active U21 < active active < encArg s < mark plus < mark and < mark isNat < mark U11 < mark U21 < mark mark < encArg s < encArg plus < encArg and < encArg isNat < encArg U11 < encArg U21 < encArg ---------------------------------------- (11) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4(+(1, n3155_4))) -> *3_4, rt in Omega(0) Induction Base: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4(+(1, 0))) Induction Step: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4(+(1, +(n3155_4, 1)))) ->_R^Omega(0) active(encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat2_4(+(1, n3155_4)))) ->_IH active(*3_4) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (12) BOUNDS(1, INF) ---------------------------------------- (13) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (14) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0) -> active(0) U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) mark(and(X1, X2)) -> active(and(mark(X1), X2)) mark(isNat(X)) -> active(isNat(X)) mark(0) -> active(0) U11(mark(X1), X2) -> U11(X1, X2) U11(X1, mark(X2)) -> U11(X1, X2) U11(active(X1), X2) -> U11(X1, X2) U11(X1, active(X2)) -> U11(X1, X2) U21(mark(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, mark(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, mark(X3)) -> U21(X1, X2, X3) U21(active(X1), X2, X3) -> U21(X1, X2, X3) U21(X1, active(X2), X3) -> U21(X1, X2, X3) U21(X1, X2, active(X3)) -> U21(X1, X2, X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0 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) active(c_isNat(0)) -> mark(tt) U21(X1, X2, c_mark(X3)) -> U21(X1, X2, X3) plus(X1, c_mark(X2)) -> plus(X1, X2) active(c_U21(tt, M, N)) -> mark(s(plus(N, M))) active(c_plus(N, c_s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) U21(c_mark(X1), X2, X3) -> U21(X1, X2, X3) isNat(c_active(X)) -> isNat(X) plus(c_active(X1), X2) -> plus(X1, X2) mark(c_s(X)) -> active(s(mark(X))) s(c_active(X)) -> s(X) and(c_active(X1), X2) -> and(X1, X2) mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) active(c_plus(N, 0)) -> mark(U11(isNat(N), N)) mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) active(c_isNat(c_s(V1))) -> mark(isNat(V1)) active(c_U11(tt, N)) -> mark(N) U11(X1, c_mark(X2)) -> U11(X1, X2) U21(X1, c_mark(X2), X3) -> U21(X1, X2, X3) s(c_mark(X)) -> s(X) plus(c_mark(X1), X2) -> plus(X1, X2) U11(c_mark(X1), X2) -> U11(X1, X2) U11(X1, c_active(X2)) -> U11(X1, X2) U21(X1, X2, c_active(X3)) -> U21(X1, X2, X3) U21(c_active(X1), X2, X3) -> U21(X1, X2, X3) active(c_and(tt, X)) -> mark(X) active(c_isNat(c_plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) mark(c_U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) mark(c_isNat(X)) -> active(isNat(X)) and(X1, c_mark(X2)) -> and(X1, X2) and(c_mark(X1), X2) -> and(X1, X2) U21(X1, c_active(X2), X3) -> U21(X1, X2, X3) plus(X1, c_active(X2)) -> plus(X1, X2) mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) U11(c_active(X1), X2) -> U11(X1, X2) isNat(c_mark(X)) -> isNat(X) 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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_mark(x_1) -> mark(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_0 -> 0 isNat(x0) -> c_isNat(x0) s(x0) -> c_s(x0) active(x0) -> c_active(x0) plus(x0, x1) -> c_plus(x0, x1) U21(x0, x1, x2) -> c_U21(x0, x1, x2) and(x0, x1) -> c_and(x0, x1) U11(x0, x1) -> c_U11(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] active(c_isNat(0)) -> mark(tt) [1] U21(X1, X2, c_mark(X3)) -> U21(X1, X2, X3) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] active(c_U21(tt, M, N)) -> mark(s(plus(N, M))) [1] active(c_plus(N, c_s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) [1] U21(c_mark(X1), X2, X3) -> U21(X1, X2, X3) [1] isNat(c_active(X)) -> isNat(X) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] s(c_active(X)) -> s(X) [1] and(c_active(X1), X2) -> and(X1, X2) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] active(c_plus(N, 0)) -> mark(U11(isNat(N), N)) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] active(c_isNat(c_s(V1))) -> mark(isNat(V1)) [1] active(c_U11(tt, N)) -> mark(N) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U21(X1, c_mark(X2), X3) -> U21(X1, X2, X3) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(c_mark(X1), X2) -> U11(X1, X2) [1] U11(X1, c_active(X2)) -> U11(X1, X2) [1] U21(X1, X2, c_active(X3)) -> U21(X1, X2, X3) [1] U21(c_active(X1), X2, X3) -> U21(X1, X2, X3) [1] active(c_and(tt, X)) -> mark(X) [1] active(c_isNat(c_plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) [1] mark(c_U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) [1] mark(c_isNat(X)) -> active(isNat(X)) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] U21(X1, c_active(X2), X3) -> U21(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U11(c_active(X1), X2) -> U11(X1, X2) [1] isNat(c_mark(X)) -> isNat(X) [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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) [0] encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_0 -> 0 [0] isNat(x0) -> c_isNat(x0) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U21(x0, x1, x2) -> c_U21(x0, x1, x2) [0] and(x0, x1) -> c_and(x0, x1) [0] U11(x0, x1) -> c_U11(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] active(c_isNat(0)) -> mark(tt) [1] U21(X1, X2, c_mark(X3)) -> U21(X1, X2, X3) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] active(c_U21(tt, M, N)) -> mark(s(plus(N, M))) [1] active(c_plus(N, c_s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) [1] U21(c_mark(X1), X2, X3) -> U21(X1, X2, X3) [1] isNat(c_active(X)) -> isNat(X) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] s(c_active(X)) -> s(X) [1] and(c_active(X1), X2) -> and(X1, X2) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] active(c_plus(N, 0)) -> mark(U11(isNat(N), N)) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] active(c_isNat(c_s(V1))) -> mark(isNat(V1)) [1] active(c_U11(tt, N)) -> mark(N) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U21(X1, c_mark(X2), X3) -> U21(X1, X2, X3) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(c_mark(X1), X2) -> U11(X1, X2) [1] U11(X1, c_active(X2)) -> U11(X1, X2) [1] U21(X1, X2, c_active(X3)) -> U21(X1, X2, X3) [1] U21(c_active(X1), X2, X3) -> U21(X1, X2, X3) [1] active(c_and(tt, X)) -> mark(X) [1] active(c_isNat(c_plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) [1] mark(c_U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) [1] mark(c_isNat(X)) -> active(isNat(X)) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] U21(X1, c_active(X2), X3) -> U21(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U11(c_active(X1), X2) -> U11(X1, X2) [1] isNat(c_mark(X)) -> isNat(X) [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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) [0] encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_0 -> 0 [0] isNat(x0) -> c_isNat(x0) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U21(x0, x1, x2) -> c_U21(x0, x1, x2) [0] and(x0, x1) -> c_and(x0, x1) [0] U11(x0, x1) -> c_U11(x0, x1) [0] mark(x0) -> c_mark(x0) [0] The TRS has the following type information: mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat 0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat c_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encArg :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat cons_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat encode_0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat 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_U11_2 encode_tt encode_mark_1 encode_U21_3 encode_s_1 encode_plus_2 encode_and_2 encode_isNat_1 encode_0 isNat_1 s_1 active_1 plus_2 U21_3 and_2 U11_2 mark_1 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_U11(v0, v1) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U21(v0, v1, v2) -> null_encode_U21 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_and(v0, v1) -> null_encode_and [0] encode_isNat(v0) -> null_encode_isNat [0] encode_0 -> null_encode_0 [0] isNat(v0) -> null_isNat [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U21(v0, v1, v2) -> null_U21 [0] and(v0, v1) -> null_and [0] U11(v0, v1) -> null_U11 [0] mark(v0) -> null_mark [0] And the following fresh constants: null_encArg, null_encode_active, null_encode_U11, null_encode_tt, null_encode_mark, null_encode_U21, null_encode_s, null_encode_plus, null_encode_and, null_encode_isNat, null_encode_0, null_isNat, null_s, null_active, null_plus, null_U21, null_and, null_U11, 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] active(c_isNat(0)) -> mark(tt) [1] U21(X1, X2, c_mark(X3)) -> U21(X1, X2, X3) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] active(c_U21(tt, M, N)) -> mark(s(plus(N, M))) [1] active(c_plus(N, c_s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) [1] U21(c_mark(X1), X2, X3) -> U21(X1, X2, X3) [1] isNat(c_active(X)) -> isNat(X) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] s(c_active(X)) -> s(X) [1] and(c_active(X1), X2) -> and(X1, X2) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] active(c_plus(N, 0)) -> mark(U11(isNat(N), N)) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] active(c_isNat(c_s(V1))) -> mark(isNat(V1)) [1] active(c_U11(tt, N)) -> mark(N) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U21(X1, c_mark(X2), X3) -> U21(X1, X2, X3) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(c_mark(X1), X2) -> U11(X1, X2) [1] U11(X1, c_active(X2)) -> U11(X1, X2) [1] U21(X1, X2, c_active(X3)) -> U21(X1, X2, X3) [1] U21(c_active(X1), X2, X3) -> U21(X1, X2, X3) [1] active(c_and(tt, X)) -> mark(X) [1] active(c_isNat(c_plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) [1] mark(c_U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) [1] mark(c_isNat(X)) -> active(isNat(X)) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] U21(X1, c_active(X2), X3) -> U21(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U11(c_active(X1), X2) -> U11(X1, X2) [1] isNat(c_mark(X)) -> isNat(X) [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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) [0] encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_0 -> 0 [0] isNat(x0) -> c_isNat(x0) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U21(x0, x1, x2) -> c_U21(x0, x1, x2) [0] and(x0, x1) -> c_and(x0, x1) [0] U11(x0, x1) -> c_U11(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_U11(v0, v1) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U21(v0, v1, v2) -> null_encode_U21 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_and(v0, v1) -> null_encode_and [0] encode_isNat(v0) -> null_encode_isNat [0] encode_0 -> null_encode_0 [0] isNat(v0) -> null_isNat [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U21(v0, v1, v2) -> null_U21 [0] and(v0, v1) -> null_and [0] U11(v0, v1) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark 0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encArg :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encArg :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11: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] active(c_isNat(0)) -> mark(tt) [1] U21(X1, X2, c_mark(X3)) -> U21(X1, X2, X3) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] active(c_U21(tt, c_mark(X2'), N)) -> mark(s(plus(N, X2'))) [2] active(c_U21(tt, M, c_active(X1'))) -> mark(s(plus(X1', M))) [2] active(c_U21(tt, M, c_mark(X1''))) -> mark(s(plus(X1'', M))) [2] active(c_U21(tt, c_active(X2''), N)) -> mark(s(plus(N, X2''))) [2] active(c_U21(tt, M, N)) -> mark(s(c_plus(N, M))) [1] active(c_U21(tt, M, N)) -> mark(s(null_plus)) [1] active(c_plus(c_active(X4), c_s(c_active(X')))) -> mark(U21(and(isNat(X'), isNat(X4)), c_active(X'), c_active(X4))) [3] active(c_plus(c_mark(X5), c_s(c_active(X')))) -> mark(U21(and(isNat(X'), isNat(X5)), c_active(X'), c_mark(X5))) [3] active(c_plus(N, c_s(c_active(X')))) -> mark(U21(and(isNat(X'), c_isNat(N)), c_active(X'), N)) [2] active(c_plus(N, c_s(c_active(X')))) -> mark(U21(and(isNat(X'), null_isNat), c_active(X'), N)) [2] active(c_plus(c_active(X6), c_s(c_mark(X'')))) -> mark(U21(and(isNat(X''), isNat(X6)), c_mark(X''), c_active(X6))) [3] active(c_plus(c_mark(X7), c_s(c_mark(X'')))) -> mark(U21(and(isNat(X''), isNat(X7)), c_mark(X''), c_mark(X7))) [3] active(c_plus(N, c_s(c_mark(X'')))) -> mark(U21(and(isNat(X''), c_isNat(N)), c_mark(X''), N)) [2] active(c_plus(N, c_s(c_mark(X'')))) -> mark(U21(and(isNat(X''), null_isNat), c_mark(X''), N)) [2] active(c_plus(c_active(X8), c_s(M))) -> mark(U21(and(c_isNat(M), isNat(X8)), M, c_active(X8))) [2] active(c_plus(c_mark(X9), c_s(M))) -> mark(U21(and(c_isNat(M), isNat(X9)), M, c_mark(X9))) [2] active(c_plus(N, c_s(M))) -> mark(U21(and(c_isNat(M), c_isNat(N)), M, N)) [1] active(c_plus(N, c_s(M))) -> mark(U21(and(c_isNat(M), null_isNat), M, N)) [1] active(c_plus(c_active(X10), c_s(M))) -> mark(U21(and(null_isNat, isNat(X10)), M, c_active(X10))) [2] active(c_plus(c_mark(X11), c_s(M))) -> mark(U21(and(null_isNat, isNat(X11)), M, c_mark(X11))) [2] active(c_plus(N, c_s(M))) -> mark(U21(and(null_isNat, c_isNat(N)), M, N)) [1] active(c_plus(N, c_s(M))) -> mark(U21(and(null_isNat, null_isNat), M, N)) [1] U21(c_mark(X1), X2, X3) -> U21(X1, X2, X3) [1] isNat(c_active(X)) -> isNat(X) [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(X12))) -> active(s(active(s(mark(X12))))) [2] mark(c_s(c_U11(X13, X21))) -> active(s(active(U11(mark(X13), X21)))) [2] mark(c_s(c_and(X14, X22))) -> active(s(active(and(mark(X14), X22)))) [2] mark(c_s(c_U21(X15, X23, X3'))) -> active(s(active(U21(mark(X15), X23, X3')))) [2] mark(c_s(c_isNat(X16))) -> active(s(active(isNat(X16)))) [2] mark(c_s(c_plus(X17, X24))) -> active(s(active(plus(mark(X17), mark(X24))))) [2] mark(c_s(X)) -> active(s(c_mark(X))) [1] mark(c_s(X)) -> active(s(null_mark)) [1] s(c_active(X)) -> s(X) [1] and(c_active(X1), X2) -> and(X1, X2) [1] mark(c_U11(tt, X2)) -> active(U11(active(tt), X2)) [2] mark(c_U11(0, X2)) -> active(U11(active(0), X2)) [2] mark(c_U11(c_s(X18), X2)) -> active(U11(active(s(mark(X18))), X2)) [2] mark(c_U11(c_U11(X19, X25), X2)) -> active(U11(active(U11(mark(X19), X25)), X2)) [2] mark(c_U11(c_and(X110, X26), X2)) -> active(U11(active(and(mark(X110), X26)), X2)) [2] mark(c_U11(c_U21(X111, X27, X3''), X2)) -> active(U11(active(U21(mark(X111), X27, X3'')), X2)) [2] mark(c_U11(c_isNat(X20), X2)) -> active(U11(active(isNat(X20)), X2)) [2] mark(c_U11(c_plus(X112, X28), X2)) -> active(U11(active(plus(mark(X112), mark(X28))), X2)) [2] mark(c_U11(X1, X2)) -> active(U11(c_mark(X1), X2)) [1] mark(c_U11(X1, X2)) -> active(U11(null_mark, X2)) [1] active(c_plus(c_active(X29), 0)) -> mark(U11(isNat(X29), c_active(X29))) [2] active(c_plus(c_mark(X30), 0)) -> mark(U11(isNat(X30), c_mark(X30))) [2] active(c_plus(N, 0)) -> mark(U11(c_isNat(N), N)) [1] active(c_plus(N, 0)) -> mark(U11(null_isNat, N)) [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(X31), X2)) -> active(and(active(s(mark(X31))), X2)) [2] mark(c_and(c_U11(X113, X210), X2)) -> active(and(active(U11(mark(X113), X210)), X2)) [2] mark(c_and(c_and(X114, X211), X2)) -> active(and(active(and(mark(X114), X211)), X2)) [2] mark(c_and(c_U21(X115, X212, X32), X2)) -> active(and(active(U21(mark(X115), X212, X32)), X2)) [2] mark(c_and(c_isNat(X33), X2)) -> active(and(active(isNat(X33)), X2)) [2] mark(c_and(c_plus(X116, X213), X2)) -> active(and(active(plus(mark(X116), mark(X213))), 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] active(c_isNat(c_s(c_active(X34)))) -> mark(isNat(X34)) [2] active(c_isNat(c_s(c_mark(X35)))) -> mark(isNat(X35)) [2] active(c_isNat(c_s(V1))) -> mark(c_isNat(V1)) [1] active(c_isNat(c_s(V1))) -> mark(null_isNat) [1] active(c_U11(tt, N)) -> mark(N) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U21(X1, c_mark(X2), X3) -> U21(X1, X2, X3) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(c_mark(X1), X2) -> U11(X1, X2) [1] U11(X1, c_active(X2)) -> U11(X1, X2) [1] U21(X1, X2, c_active(X3)) -> U21(X1, X2, X3) [1] U21(c_active(X1), X2, X3) -> U21(X1, X2, X3) [1] active(c_and(tt, X)) -> mark(X) [1] active(c_isNat(c_plus(c_active(X36), c_active(X38)))) -> mark(and(isNat(X36), isNat(X38))) [3] active(c_isNat(c_plus(c_active(X36), c_mark(X39)))) -> mark(and(isNat(X36), isNat(X39))) [3] active(c_isNat(c_plus(c_active(X36), V2))) -> mark(and(isNat(X36), c_isNat(V2))) [2] active(c_isNat(c_plus(c_active(X36), V2))) -> mark(and(isNat(X36), null_isNat)) [2] active(c_isNat(c_plus(c_mark(X37), c_active(X40)))) -> mark(and(isNat(X37), isNat(X40))) [3] active(c_isNat(c_plus(c_mark(X37), c_mark(X41)))) -> mark(and(isNat(X37), isNat(X41))) [3] active(c_isNat(c_plus(c_mark(X37), V2))) -> mark(and(isNat(X37), c_isNat(V2))) [2] active(c_isNat(c_plus(c_mark(X37), V2))) -> mark(and(isNat(X37), null_isNat)) [2] active(c_isNat(c_plus(V1, c_active(X42)))) -> mark(and(c_isNat(V1), isNat(X42))) [2] active(c_isNat(c_plus(V1, c_mark(X43)))) -> mark(and(c_isNat(V1), isNat(X43))) [2] active(c_isNat(c_plus(V1, V2))) -> mark(and(c_isNat(V1), c_isNat(V2))) [1] active(c_isNat(c_plus(V1, V2))) -> mark(and(c_isNat(V1), null_isNat)) [1] active(c_isNat(c_plus(V1, c_active(X44)))) -> mark(and(null_isNat, isNat(X44))) [2] active(c_isNat(c_plus(V1, c_mark(X45)))) -> mark(and(null_isNat, isNat(X45))) [2] active(c_isNat(c_plus(V1, V2))) -> mark(and(null_isNat, c_isNat(V2))) [1] active(c_isNat(c_plus(V1, V2))) -> mark(and(null_isNat, null_isNat)) [1] mark(c_U21(tt, X2, X3)) -> active(U21(active(tt), X2, X3)) [2] mark(c_U21(0, X2, X3)) -> active(U21(active(0), X2, X3)) [2] mark(c_U21(c_s(X46), X2, X3)) -> active(U21(active(s(mark(X46))), X2, X3)) [2] mark(c_U21(c_U11(X117, X214), X2, X3)) -> active(U21(active(U11(mark(X117), X214)), X2, X3)) [2] mark(c_U21(c_and(X118, X215), X2, X3)) -> active(U21(active(and(mark(X118), X215)), X2, X3)) [2] mark(c_U21(c_U21(X119, X216, X310), X2, X3)) -> active(U21(active(U21(mark(X119), X216, X310)), X2, X3)) [2] mark(c_U21(c_isNat(X47), X2, X3)) -> active(U21(active(isNat(X47)), X2, X3)) [2] mark(c_U21(c_plus(X120, X217), X2, X3)) -> active(U21(active(plus(mark(X120), mark(X217))), X2, X3)) [2] mark(c_U21(X1, X2, X3)) -> active(U21(c_mark(X1), X2, X3)) [1] mark(c_U21(X1, X2, X3)) -> active(U21(null_mark, X2, X3)) [1] mark(c_isNat(c_active(X48))) -> active(isNat(X48)) [2] mark(c_isNat(c_mark(X49))) -> active(isNat(X49)) [2] mark(c_isNat(X)) -> active(c_isNat(X)) [1] mark(c_isNat(X)) -> active(null_isNat) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] U21(X1, c_active(X2), X3) -> U21(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U11(c_active(X1), X2) -> U11(X1, X2) [1] isNat(c_mark(X)) -> isNat(X) [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_U11(x_11, x_2'))) -> active(U11(encArg(x_11), encArg(x_2'))) [0] encArg(cons_active(cons_U21(x_12, x_2'', x_3'))) -> active(U21(encArg(x_12), encArg(x_2''), encArg(x_3'))) [0] encArg(cons_active(cons_s(x_13))) -> active(s(encArg(x_13))) [0] encArg(cons_active(cons_plus(x_14, x_21))) -> active(plus(encArg(x_14), encArg(x_21))) [0] encArg(cons_active(cons_and(x_15, x_22))) -> active(and(encArg(x_15), encArg(x_22))) [0] encArg(cons_active(cons_isNat(x_16))) -> active(isNat(encArg(x_16))) [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_17))) -> mark(active(encArg(x_17))) [0] encArg(cons_mark(cons_mark(x_18))) -> mark(mark(encArg(x_18))) [0] encArg(cons_mark(cons_U11(x_19, x_23))) -> mark(U11(encArg(x_19), encArg(x_23))) [0] encArg(cons_mark(cons_U21(x_110, x_24, x_3''))) -> mark(U21(encArg(x_110), encArg(x_24), encArg(x_3''))) [0] encArg(cons_mark(cons_s(x_111))) -> mark(s(encArg(x_111))) [0] encArg(cons_mark(cons_plus(x_112, x_25))) -> mark(plus(encArg(x_112), encArg(x_25))) [0] encArg(cons_mark(cons_and(x_113, x_26))) -> mark(and(encArg(x_113), encArg(x_26))) [0] encArg(cons_mark(cons_isNat(x_114))) -> mark(isNat(encArg(x_114))) [0] encArg(cons_mark(x_1)) -> mark(null_encArg) [0] encArg(cons_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) [0] encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_s(tt)) -> s(tt) [0] encArg(cons_s(0)) -> s(0) [0] encArg(cons_s(cons_active(x_11175))) -> s(active(encArg(x_11175))) [0] encArg(cons_s(cons_mark(x_11176))) -> s(mark(encArg(x_11176))) [0] encArg(cons_s(cons_U11(x_11177, x_2587))) -> s(U11(encArg(x_11177), encArg(x_2587))) [0] encArg(cons_s(cons_U21(x_11178, x_2588, x_3146))) -> s(U21(encArg(x_11178), encArg(x_2588), encArg(x_3146))) [0] encArg(cons_s(cons_s(x_11179))) -> s(s(encArg(x_11179))) [0] encArg(cons_s(cons_plus(x_11180, x_2589))) -> s(plus(encArg(x_11180), encArg(x_2589))) [0] encArg(cons_s(cons_and(x_11181, x_2590))) -> s(and(encArg(x_11181), encArg(x_2590))) [0] encArg(cons_s(cons_isNat(x_11182))) -> s(isNat(encArg(x_11182))) [0] encArg(cons_s(x_1)) -> s(null_encArg) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_isNat(tt)) -> isNat(tt) [0] encArg(cons_isNat(0)) -> isNat(0) [0] encArg(cons_isNat(cons_active(x_11375))) -> isNat(active(encArg(x_11375))) [0] encArg(cons_isNat(cons_mark(x_11376))) -> isNat(mark(encArg(x_11376))) [0] encArg(cons_isNat(cons_U11(x_11377, x_2687))) -> isNat(U11(encArg(x_11377), encArg(x_2687))) [0] encArg(cons_isNat(cons_U21(x_11378, x_2688, x_3171))) -> isNat(U21(encArg(x_11378), encArg(x_2688), encArg(x_3171))) [0] encArg(cons_isNat(cons_s(x_11379))) -> isNat(s(encArg(x_11379))) [0] encArg(cons_isNat(cons_plus(x_11380, x_2689))) -> isNat(plus(encArg(x_11380), encArg(x_2689))) [0] encArg(cons_isNat(cons_and(x_11381, x_2690))) -> isNat(and(encArg(x_11381), encArg(x_2690))) [0] encArg(cons_isNat(cons_isNat(x_11382))) -> isNat(isNat(encArg(x_11382))) [0] encArg(cons_isNat(x_1)) -> isNat(null_encArg) [0] encode_active(tt) -> active(tt) [0] encode_active(0) -> active(0) [0] encode_active(cons_active(x_11383)) -> active(active(encArg(x_11383))) [0] encode_active(cons_mark(x_11384)) -> active(mark(encArg(x_11384))) [0] encode_active(cons_U11(x_11385, x_2691)) -> active(U11(encArg(x_11385), encArg(x_2691))) [0] encode_active(cons_U21(x_11386, x_2692, x_3172)) -> active(U21(encArg(x_11386), encArg(x_2692), encArg(x_3172))) [0] encode_active(cons_s(x_11387)) -> active(s(encArg(x_11387))) [0] encode_active(cons_plus(x_11388, x_2693)) -> active(plus(encArg(x_11388), encArg(x_2693))) [0] encode_active(cons_and(x_11389, x_2694)) -> active(and(encArg(x_11389), encArg(x_2694))) [0] encode_active(cons_isNat(x_11390)) -> active(isNat(encArg(x_11390))) [0] encode_active(x_1) -> active(null_encArg) [0] encode_U11(x_1, x_2) -> U11(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_11487)) -> mark(active(encArg(x_11487))) [0] encode_mark(cons_mark(x_11488)) -> mark(mark(encArg(x_11488))) [0] encode_mark(cons_U11(x_11489, x_2743)) -> mark(U11(encArg(x_11489), encArg(x_2743))) [0] encode_mark(cons_U21(x_11490, x_2744, x_3185)) -> mark(U21(encArg(x_11490), encArg(x_2744), encArg(x_3185))) [0] encode_mark(cons_s(x_11491)) -> mark(s(encArg(x_11491))) [0] encode_mark(cons_plus(x_11492, x_2745)) -> mark(plus(encArg(x_11492), encArg(x_2745))) [0] encode_mark(cons_and(x_11493, x_2746)) -> mark(and(encArg(x_11493), encArg(x_2746))) [0] encode_mark(cons_isNat(x_11494)) -> mark(isNat(encArg(x_11494))) [0] encode_mark(x_1) -> mark(null_encArg) [0] encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_s(tt) -> s(tt) [0] encode_s(0) -> s(0) [0] encode_s(cons_active(x_12559)) -> s(active(encArg(x_12559))) [0] encode_s(cons_mark(x_12560)) -> s(mark(encArg(x_12560))) [0] encode_s(cons_U11(x_12561, x_21279)) -> s(U11(encArg(x_12561), encArg(x_21279))) [0] encode_s(cons_U21(x_12562, x_21280, x_3319)) -> s(U21(encArg(x_12562), encArg(x_21280), encArg(x_3319))) [0] encode_s(cons_s(x_12563)) -> s(s(encArg(x_12563))) [0] encode_s(cons_plus(x_12564, x_21281)) -> s(plus(encArg(x_12564), encArg(x_21281))) [0] encode_s(cons_and(x_12565, x_21282)) -> s(and(encArg(x_12565), encArg(x_21282))) [0] encode_s(cons_isNat(x_12566)) -> s(isNat(encArg(x_12566))) [0] encode_s(x_1) -> s(null_encArg) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_isNat(tt) -> isNat(tt) [0] encode_isNat(0) -> isNat(0) [0] encode_isNat(cons_active(x_12759)) -> isNat(active(encArg(x_12759))) [0] encode_isNat(cons_mark(x_12760)) -> isNat(mark(encArg(x_12760))) [0] encode_isNat(cons_U11(x_12761, x_21379)) -> isNat(U11(encArg(x_12761), encArg(x_21379))) [0] encode_isNat(cons_U21(x_12762, x_21380, x_3344)) -> isNat(U21(encArg(x_12762), encArg(x_21380), encArg(x_3344))) [0] encode_isNat(cons_s(x_12763)) -> isNat(s(encArg(x_12763))) [0] encode_isNat(cons_plus(x_12764, x_21381)) -> isNat(plus(encArg(x_12764), encArg(x_21381))) [0] encode_isNat(cons_and(x_12765, x_21382)) -> isNat(and(encArg(x_12765), encArg(x_21382))) [0] encode_isNat(cons_isNat(x_12766)) -> isNat(isNat(encArg(x_12766))) [0] encode_isNat(x_1) -> isNat(null_encArg) [0] encode_0 -> 0 [0] isNat(x0) -> c_isNat(x0) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U21(x0, x1, x2) -> c_U21(x0, x1, x2) [0] and(x0, x1) -> c_and(x0, x1) [0] U11(x0, x1) -> c_U11(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_U11(v0, v1) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U21(v0, v1, v2) -> null_encode_U21 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_and(v0, v1) -> null_encode_and [0] encode_isNat(v0) -> null_encode_isNat [0] encode_0 -> null_encode_0 [0] isNat(v0) -> null_isNat [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U21(v0, v1, v2) -> null_U21 [0] and(v0, v1) -> null_and [0] U11(v0, v1) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark 0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encArg :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encArg :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11: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_U11 => 0 null_encode_tt => 0 null_encode_mark => 0 null_encode_U21 => 0 null_encode_s => 0 null_encode_plus => 0 null_encode_and => 0 null_encode_isNat => 0 null_encode_0 => 0 null_isNat => 0 null_s => 0 null_active => 0 null_plus => 0 null_U21 => 0 null_and => 0 null_U11 => 0 null_mark => 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: U11(z, z') -{ 1 }-> U11(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 U11(z, z') -{ 1 }-> U11(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 U11(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 U21(z, z', z'') -{ 1 }-> U21(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U21(z, z', z'') -{ 1 }-> U21(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U21(z, z', z'') -{ 1 }-> U21(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U21(z, z', z'') -{ 0 }-> 1 + x0 + x1 + x2 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1, z'' = x2, x2 >= 0 active(z) -{ 1 }-> mark(N) :|: z = 1 + 1 + N, N >= 0 active(z) -{ 1 }-> mark(X) :|: z = 1 + 1 + X, X >= 0 active(z) -{ 2 }-> mark(s(plus(N, X2'))) :|: X2' >= 0, z = 1 + 1 + (1 + X2') + N, N >= 0 active(z) -{ 2 }-> mark(s(plus(N, X2''))) :|: z = 1 + 1 + (1 + X2'') + N, X2'' >= 0, N >= 0 active(z) -{ 2 }-> mark(s(plus(X1', M))) :|: X1' >= 0, z = 1 + 1 + M + (1 + X1'), M >= 0 active(z) -{ 2 }-> mark(s(plus(X1'', M))) :|: X1'' >= 0, z = 1 + 1 + M + (1 + X1''), M >= 0 active(z) -{ 1 }-> mark(s(0)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(s(1 + N + M)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 2 }-> mark(isNat(X34)) :|: z = 1 + (1 + (1 + X34)), X34 >= 0 active(z) -{ 2 }-> mark(isNat(X35)) :|: X35 >= 0, z = 1 + (1 + (1 + X35)) active(z) -{ 3 }-> mark(and(isNat(X36), isNat(X38))) :|: z = 1 + (1 + (1 + X36) + (1 + X38)), X36 >= 0, X38 >= 0 active(z) -{ 3 }-> mark(and(isNat(X36), isNat(X39))) :|: X36 >= 0, z = 1 + (1 + (1 + X36) + (1 + X39)), X39 >= 0 active(z) -{ 2 }-> mark(and(isNat(X36), 0)) :|: X36 >= 0, V2 >= 0, z = 1 + (1 + (1 + X36) + V2) active(z) -{ 2 }-> mark(and(isNat(X36), 1 + V2)) :|: X36 >= 0, V2 >= 0, z = 1 + (1 + (1 + X36) + V2) active(z) -{ 3 }-> mark(and(isNat(X37), isNat(X40))) :|: z = 1 + (1 + (1 + X37) + (1 + X40)), X37 >= 0, X40 >= 0 active(z) -{ 3 }-> mark(and(isNat(X37), isNat(X41))) :|: X37 >= 0, X41 >= 0, z = 1 + (1 + (1 + X37) + (1 + X41)) active(z) -{ 2 }-> mark(and(isNat(X37), 0)) :|: X37 >= 0, z = 1 + (1 + (1 + X37) + V2), V2 >= 0 active(z) -{ 2 }-> mark(and(isNat(X37), 1 + V2)) :|: X37 >= 0, z = 1 + (1 + (1 + X37) + V2), V2 >= 0 active(z) -{ 2 }-> mark(and(0, isNat(X44))) :|: V1 >= 0, z = 1 + (1 + V1 + (1 + X44)), X44 >= 0 active(z) -{ 2 }-> mark(and(0, isNat(X45))) :|: z = 1 + (1 + V1 + (1 + X45)), V1 >= 0, X45 >= 0 active(z) -{ 1 }-> mark(and(0, 0)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 1 }-> mark(and(0, 1 + V2)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 2 }-> mark(and(1 + V1, isNat(X42))) :|: V1 >= 0, z = 1 + (1 + V1 + (1 + X42)), X42 >= 0 active(z) -{ 2 }-> mark(and(1 + V1, isNat(X43))) :|: z = 1 + (1 + V1 + (1 + X43)), X43 >= 0, V1 >= 0 active(z) -{ 1 }-> mark(and(1 + V1, 0)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 1 }-> mark(and(1 + V1, 1 + V2)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 3 }-> mark(U21(and(isNat(X'), isNat(X4)), 1 + X', 1 + X4)) :|: z = 1 + (1 + X4) + (1 + (1 + X')), X' >= 0, X4 >= 0 active(z) -{ 3 }-> mark(U21(and(isNat(X'), isNat(X5)), 1 + X', 1 + X5)) :|: X5 >= 0, z = 1 + (1 + X5) + (1 + (1 + X')), X' >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X'), 0), 1 + X', N)) :|: z = 1 + N + (1 + (1 + X')), X' >= 0, N >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X'), 1 + N), 1 + X', N)) :|: z = 1 + N + (1 + (1 + X')), X' >= 0, N >= 0 active(z) -{ 3 }-> mark(U21(and(isNat(X''), isNat(X6)), 1 + X'', 1 + X6)) :|: z = 1 + (1 + X6) + (1 + (1 + X'')), X6 >= 0, X'' >= 0 active(z) -{ 3 }-> mark(U21(and(isNat(X''), isNat(X7)), 1 + X'', 1 + X7)) :|: z = 1 + (1 + X7) + (1 + (1 + X'')), X7 >= 0, X'' >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X''), 0), 1 + X'', N)) :|: X'' >= 0, z = 1 + N + (1 + (1 + X'')), N >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X''), 1 + N), 1 + X'', N)) :|: X'' >= 0, z = 1 + N + (1 + (1 + X'')), N >= 0 active(z) -{ 2 }-> mark(U21(and(0, isNat(X10)), M, 1 + X10)) :|: z = 1 + (1 + X10) + (1 + M), X10 >= 0, M >= 0 active(z) -{ 2 }-> mark(U21(and(0, isNat(X11)), M, 1 + X11)) :|: X11 >= 0, z = 1 + (1 + X11) + (1 + M), M >= 0 active(z) -{ 1 }-> mark(U21(and(0, 0), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(U21(and(0, 1 + N), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 2 }-> mark(U21(and(1 + M, isNat(X8)), M, 1 + X8)) :|: X8 >= 0, M >= 0, z = 1 + (1 + X8) + (1 + M) active(z) -{ 2 }-> mark(U21(and(1 + M, isNat(X9)), M, 1 + X9)) :|: X9 >= 0, z = 1 + (1 + X9) + (1 + M), M >= 0 active(z) -{ 1 }-> mark(U21(and(1 + M, 0), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(U21(and(1 + M, 1 + N), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 2 }-> mark(U11(isNat(X29), 1 + X29)) :|: z = 1 + (1 + X29) + 0, X29 >= 0 active(z) -{ 2 }-> mark(U11(isNat(X30), 1 + X30)) :|: z = 1 + (1 + X30) + 0, X30 >= 0 active(z) -{ 1 }-> mark(U11(0, N)) :|: z = 1 + N + 0, N >= 0 active(z) -{ 1 }-> mark(U11(1 + N, N)) :|: z = 1 + N + 0, N >= 0 active(z) -{ 1 }-> mark(1) :|: z = 1 + 0 active(z) -{ 1 }-> mark(0) :|: V1 >= 0, z = 1 + (1 + V1) active(z) -{ 1 }-> mark(1 + V1) :|: V1 >= 0, z = 1 + (1 + V1) 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 }-> s(s(encArg(x_11179))) :|: z = 1 + (1 + x_11179), x_11179 >= 0 encArg(z) -{ 0 }-> s(plus(encArg(x_11180), encArg(x_2589))) :|: z = 1 + (1 + x_11180 + x_2589), x_11180 >= 0, x_2589 >= 0 encArg(z) -{ 0 }-> s(mark(encArg(x_11176))) :|: x_11176 >= 0, z = 1 + (1 + x_11176) encArg(z) -{ 0 }-> s(isNat(encArg(x_11182))) :|: x_11182 >= 0, z = 1 + (1 + x_11182) encArg(z) -{ 0 }-> s(and(encArg(x_11181), encArg(x_2590))) :|: z = 1 + (1 + x_11181 + x_2590), x_2590 >= 0, x_11181 >= 0 encArg(z) -{ 0 }-> s(active(encArg(x_11175))) :|: z = 1 + (1 + x_11175), x_11175 >= 0 encArg(z) -{ 0 }-> s(U21(encArg(x_11178), encArg(x_2588), encArg(x_3146))) :|: x_11178 >= 0, x_3146 >= 0, x_2588 >= 0, z = 1 + (1 + x_11178 + x_2588 + x_3146) encArg(z) -{ 0 }-> s(U11(encArg(x_11177), encArg(x_2587))) :|: x_2587 >= 0, x_11177 >= 0, z = 1 + (1 + x_11177 + x_2587) 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(s(encArg(x_111))) :|: z = 1 + (1 + x_111), x_111 >= 0 encArg(z) -{ 0 }-> mark(plus(encArg(x_112), encArg(x_25))) :|: x_25 >= 0, z = 1 + (1 + x_112 + x_25), x_112 >= 0 encArg(z) -{ 0 }-> mark(mark(encArg(x_18))) :|: z = 1 + (1 + x_18), x_18 >= 0 encArg(z) -{ 0 }-> mark(isNat(encArg(x_114))) :|: z = 1 + (1 + x_114), x_114 >= 0 encArg(z) -{ 0 }-> mark(and(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(x_17))) :|: x_17 >= 0, z = 1 + (1 + x_17) encArg(z) -{ 0 }-> mark(U21(encArg(x_110), encArg(x_24), encArg(x_3''))) :|: x_24 >= 0, z = 1 + (1 + x_110 + x_24 + x_3''), x_110 >= 0, x_3'' >= 0 encArg(z) -{ 0 }-> mark(U11(encArg(x_19), encArg(x_23))) :|: z = 1 + (1 + x_19 + x_23), x_23 >= 0, x_19 >= 0 encArg(z) -{ 0 }-> mark(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> mark(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> isNat(s(encArg(x_11379))) :|: z = 1 + (1 + x_11379), x_11379 >= 0 encArg(z) -{ 0 }-> isNat(plus(encArg(x_11380), encArg(x_2689))) :|: x_11380 >= 0, z = 1 + (1 + x_11380 + x_2689), x_2689 >= 0 encArg(z) -{ 0 }-> isNat(mark(encArg(x_11376))) :|: z = 1 + (1 + x_11376), x_11376 >= 0 encArg(z) -{ 0 }-> isNat(isNat(encArg(x_11382))) :|: z = 1 + (1 + x_11382), x_11382 >= 0 encArg(z) -{ 0 }-> isNat(and(encArg(x_11381), encArg(x_2690))) :|: z = 1 + (1 + x_11381 + x_2690), x_11381 >= 0, x_2690 >= 0 encArg(z) -{ 0 }-> isNat(active(encArg(x_11375))) :|: x_11375 >= 0, z = 1 + (1 + x_11375) encArg(z) -{ 0 }-> isNat(U21(encArg(x_11378), encArg(x_2688), encArg(x_3171))) :|: x_3171 >= 0, z = 1 + (1 + x_11378 + x_2688 + x_3171), x_11378 >= 0, x_2688 >= 0 encArg(z) -{ 0 }-> isNat(U11(encArg(x_11377), encArg(x_2687))) :|: x_11377 >= 0, z = 1 + (1 + x_11377 + x_2687), x_2687 >= 0 encArg(z) -{ 0 }-> isNat(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> isNat(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> isNat(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(s(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0 encArg(z) -{ 0 }-> active(plus(encArg(x_14), encArg(x_21))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> active(isNat(encArg(x_16))) :|: x_16 >= 0, z = 1 + (1 + x_16) encArg(z) -{ 0 }-> active(and(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15 + x_22), x_22 >= 0 encArg(z) -{ 0 }-> active(active(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> active(U21(encArg(x_12), encArg(x_2''), encArg(x_3'))) :|: x_3' >= 0, x_2'' >= 0, x_12 >= 0, z = 1 + (1 + x_12 + x_2'' + x_3') encArg(z) -{ 0 }-> active(U11(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2') 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 }-> U21(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> U11(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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_U11(z, z') -{ 0 }-> U11(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_U21(z, z', z'') -{ 0 }-> U21(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_active(z) -{ 0 }-> active(s(encArg(x_11387))) :|: z = 1 + x_11387, x_11387 >= 0 encode_active(z) -{ 0 }-> active(plus(encArg(x_11388), encArg(x_2693))) :|: x_2693 >= 0, x_11388 >= 0, z = 1 + x_11388 + x_2693 encode_active(z) -{ 0 }-> active(mark(encArg(x_11384))) :|: z = 1 + x_11384, x_11384 >= 0 encode_active(z) -{ 0 }-> active(isNat(encArg(x_11390))) :|: x_11390 >= 0, z = 1 + x_11390 encode_active(z) -{ 0 }-> active(and(encArg(x_11389), encArg(x_2694))) :|: x_2694 >= 0, z = 1 + x_11389 + x_2694, x_11389 >= 0 encode_active(z) -{ 0 }-> active(active(encArg(x_11383))) :|: z = 1 + x_11383, x_11383 >= 0 encode_active(z) -{ 0 }-> active(U21(encArg(x_11386), encArg(x_2692), encArg(x_3172))) :|: x_2692 >= 0, x_11386 >= 0, z = 1 + x_11386 + x_2692 + x_3172, x_3172 >= 0 encode_active(z) -{ 0 }-> active(U11(encArg(x_11385), encArg(x_2691))) :|: x_11385 >= 0, z = 1 + x_11385 + x_2691, x_2691 >= 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_isNat(z) -{ 0 }-> isNat(s(encArg(x_12763))) :|: x_12763 >= 0, z = 1 + x_12763 encode_isNat(z) -{ 0 }-> isNat(plus(encArg(x_12764), encArg(x_21381))) :|: x_12764 >= 0, x_21381 >= 0, z = 1 + x_12764 + x_21381 encode_isNat(z) -{ 0 }-> isNat(mark(encArg(x_12760))) :|: z = 1 + x_12760, x_12760 >= 0 encode_isNat(z) -{ 0 }-> isNat(isNat(encArg(x_12766))) :|: x_12766 >= 0, z = 1 + x_12766 encode_isNat(z) -{ 0 }-> isNat(and(encArg(x_12765), encArg(x_21382))) :|: x_12765 >= 0, x_21382 >= 0, z = 1 + x_12765 + x_21382 encode_isNat(z) -{ 0 }-> isNat(active(encArg(x_12759))) :|: z = 1 + x_12759, x_12759 >= 0 encode_isNat(z) -{ 0 }-> isNat(U21(encArg(x_12762), encArg(x_21380), encArg(x_3344))) :|: x_21380 >= 0, x_3344 >= 0, x_12762 >= 0, z = 1 + x_12762 + x_21380 + x_3344 encode_isNat(z) -{ 0 }-> isNat(U11(encArg(x_12761), encArg(x_21379))) :|: z = 1 + x_12761 + x_21379, x_12761 >= 0, x_21379 >= 0 encode_isNat(z) -{ 0 }-> isNat(1) :|: z = 1 encode_isNat(z) -{ 0 }-> isNat(0) :|: z = 0 encode_isNat(z) -{ 0 }-> isNat(0) :|: x_1 >= 0, z = x_1 encode_isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_mark(z) -{ 0 }-> mark(s(encArg(x_11491))) :|: z = 1 + x_11491, x_11491 >= 0 encode_mark(z) -{ 0 }-> mark(plus(encArg(x_11492), encArg(x_2745))) :|: x_11492 >= 0, z = 1 + x_11492 + x_2745, x_2745 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(x_11488))) :|: x_11488 >= 0, z = 1 + x_11488 encode_mark(z) -{ 0 }-> mark(isNat(encArg(x_11494))) :|: x_11494 >= 0, z = 1 + x_11494 encode_mark(z) -{ 0 }-> mark(and(encArg(x_11493), encArg(x_2746))) :|: x_11493 >= 0, z = 1 + x_11493 + x_2746, x_2746 >= 0 encode_mark(z) -{ 0 }-> mark(active(encArg(x_11487))) :|: z = 1 + x_11487, x_11487 >= 0 encode_mark(z) -{ 0 }-> mark(U21(encArg(x_11490), encArg(x_2744), encArg(x_3185))) :|: x_2744 >= 0, x_3185 >= 0, x_11490 >= 0, z = 1 + x_11490 + x_2744 + x_3185 encode_mark(z) -{ 0 }-> mark(U11(encArg(x_11489), encArg(x_2743))) :|: x_2743 >= 0, z = 1 + x_11489 + x_2743, x_11489 >= 0 encode_mark(z) -{ 0 }-> mark(1) :|: z = 1 encode_mark(z) -{ 0 }-> mark(0) :|: z = 0 encode_mark(z) -{ 0 }-> mark(0) :|: x_1 >= 0, z = x_1 encode_mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_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(s(encArg(x_12563))) :|: z = 1 + x_12563, x_12563 >= 0 encode_s(z) -{ 0 }-> s(plus(encArg(x_12564), encArg(x_21281))) :|: x_21281 >= 0, z = 1 + x_12564 + x_21281, x_12564 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(x_12560))) :|: x_12560 >= 0, z = 1 + x_12560 encode_s(z) -{ 0 }-> s(isNat(encArg(x_12566))) :|: z = 1 + x_12566, x_12566 >= 0 encode_s(z) -{ 0 }-> s(and(encArg(x_12565), encArg(x_21282))) :|: x_12565 >= 0, x_21282 >= 0, z = 1 + x_12565 + x_21282 encode_s(z) -{ 0 }-> s(active(encArg(x_12559))) :|: x_12559 >= 0, z = 1 + x_12559 encode_s(z) -{ 0 }-> s(U21(encArg(x_12562), encArg(x_21280), encArg(x_3319))) :|: z = 1 + x_12562 + x_21280 + x_3319, x_3319 >= 0, x_12562 >= 0, x_21280 >= 0 encode_s(z) -{ 0 }-> s(U11(encArg(x_12561), encArg(x_21279))) :|: x_21279 >= 0, x_12561 >= 0, z = 1 + x_12561 + x_21279 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 :|: isNat(z) -{ 1 }-> isNat(X) :|: z = 1 + X, X >= 0 isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 isNat(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 mark(z) -{ 2 }-> active(s(active(s(mark(X12))))) :|: z = 1 + (1 + X12), X12 >= 0 mark(z) -{ 2 }-> active(s(active(plus(mark(X17), mark(X24))))) :|: z = 1 + (1 + X17 + X24), X17 >= 0, X24 >= 0 mark(z) -{ 2 }-> active(s(active(isNat(X16)))) :|: X16 >= 0, z = 1 + (1 + X16) mark(z) -{ 2 }-> active(s(active(and(mark(X14), X22)))) :|: z = 1 + (1 + X14 + X22), X22 >= 0, X14 >= 0 mark(z) -{ 2 }-> active(s(active(U21(mark(X15), X23, X3')))) :|: X3' >= 0, X15 >= 0, X23 >= 0, z = 1 + (1 + X15 + X23 + X3') mark(z) -{ 2 }-> active(s(active(U11(mark(X13), X21)))) :|: X21 >= 0, X13 >= 0, z = 1 + (1 + X13 + X21) 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(isNat(X48)) :|: z = 1 + (1 + X48), X48 >= 0 mark(z) -{ 2 }-> active(isNat(X49)) :|: z = 1 + (1 + X49), X49 >= 0 mark(z) -{ 2 }-> active(and(active(s(mark(X31))), X2)) :|: z = 1 + (1 + X31) + X2, X31 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(plus(mark(X116), mark(X213))), X2)) :|: z = 1 + (1 + X116 + X213) + X2, X213 >= 0, X116 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(isNat(X33)), X2)) :|: X33 >= 0, z = 1 + (1 + X33) + X2, X2 >= 0 mark(z) -{ 2 }-> active(and(active(and(mark(X114), X211)), X2)) :|: X114 >= 0, z = 1 + (1 + X114 + X211) + X2, X211 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(U21(mark(X115), X212, X32)), X2)) :|: X212 >= 0, X32 >= 0, X115 >= 0, X2 >= 0, z = 1 + (1 + X115 + X212 + X32) + X2 mark(z) -{ 2 }-> active(and(active(U11(mark(X113), X210)), X2)) :|: X113 >= 0, z = 1 + (1 + X113 + X210) + X2, X2 >= 0, X210 >= 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) -{ 2 }-> active(U21(active(s(mark(X46))), X2, X3)) :|: X3 >= 0, X46 >= 0, X2 >= 0, z = 1 + (1 + X46) + X2 + X3 mark(z) -{ 2 }-> active(U21(active(plus(mark(X120), mark(X217))), X2, X3)) :|: X120 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X120 + X217) + X2 + X3, X217 >= 0 mark(z) -{ 2 }-> active(U21(active(isNat(X47)), X2, X3)) :|: z = 1 + (1 + X47) + X2 + X3, X47 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(and(mark(X118), X215)), X2, X3)) :|: z = 1 + (1 + X118 + X215) + X2 + X3, X118 >= 0, X3 >= 0, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(U21(mark(X119), X216, X310)), X2, X3)) :|: X216 >= 0, X3 >= 0, X310 >= 0, X2 >= 0, z = 1 + (1 + X119 + X216 + X310) + X2 + X3, X119 >= 0 mark(z) -{ 2 }-> active(U21(active(U11(mark(X117), X214)), X2, X3)) :|: X117 >= 0, X214 >= 0, X3 >= 0, z = 1 + (1 + X117 + X214) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(1), X2, X3)) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(0), X2, X3)) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 1 }-> active(U21(0, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U21(1 + X1, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(s(mark(X18))), X2)) :|: z = 1 + (1 + X18) + X2, X18 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(plus(mark(X112), mark(X28))), X2)) :|: z = 1 + (1 + X112 + X28) + X2, X28 >= 0, X112 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(isNat(X20)), X2)) :|: z = 1 + (1 + X20) + X2, X20 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(and(mark(X110), X26)), X2)) :|: X110 >= 0, z = 1 + (1 + X110 + X26) + X2, X26 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(U21(mark(X111), X27, X3'')), X2)) :|: X27 >= 0, X3'' >= 0, z = 1 + (1 + X111 + X27 + X3'') + X2, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> active(U11(active(U11(mark(X19), X25)), X2)) :|: z = 1 + (1 + X19 + X25) + X2, X19 >= 0, X2 >= 0, X25 >= 0 mark(z) -{ 2 }-> active(U11(active(1), X2)) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(0), X2)) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 1 }-> active(U11(0, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(U11(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) -{ 1 }-> active(0) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(1 + X) :|: z = 1 + X, X >= 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 ---------------------------------------- (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: U11(z, z') -{ 1 }-> U11(z, z' - 1) :|: z >= 0, z' - 1 >= 0 U11(z, z') -{ 1 }-> U11(z - 1, z') :|: z - 1 >= 0, z' >= 0 U11(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 U11(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 U21(z, z', z'') -{ 1 }-> U21(z, z', z'' - 1) :|: z >= 0, z'' - 1 >= 0, z' >= 0 U21(z, z', z'') -{ 1 }-> U21(z, z' - 1, z'') :|: z >= 0, z'' >= 0, z' - 1 >= 0 U21(z, z', z'') -{ 1 }-> U21(z - 1, z', z'') :|: z - 1 >= 0, z'' >= 0, z' >= 0 U21(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 U21(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z >= 0, z' >= 0, z'' >= 0 active(z) -{ 2 }-> mark(s(plus(N, X2'))) :|: X2' >= 0, z = 1 + 1 + (1 + X2') + N, N >= 0 active(z) -{ 2 }-> mark(s(plus(N, X2''))) :|: z = 1 + 1 + (1 + X2'') + N, X2'' >= 0, N >= 0 active(z) -{ 2 }-> mark(s(plus(X1', M))) :|: X1' >= 0, z = 1 + 1 + M + (1 + X1'), M >= 0 active(z) -{ 2 }-> mark(s(plus(X1'', M))) :|: X1'' >= 0, z = 1 + 1 + M + (1 + X1''), M >= 0 active(z) -{ 1 }-> mark(s(0)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(s(1 + N + M)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 2 }-> mark(isNat(z - 3)) :|: z - 3 >= 0 active(z) -{ 3 }-> mark(and(isNat(X36), isNat(X38))) :|: z = 1 + (1 + (1 + X36) + (1 + X38)), X36 >= 0, X38 >= 0 active(z) -{ 3 }-> mark(and(isNat(X36), isNat(X39))) :|: X36 >= 0, z = 1 + (1 + (1 + X36) + (1 + X39)), X39 >= 0 active(z) -{ 2 }-> mark(and(isNat(X36), 0)) :|: X36 >= 0, V2 >= 0, z = 1 + (1 + (1 + X36) + V2) active(z) -{ 2 }-> mark(and(isNat(X36), 1 + V2)) :|: X36 >= 0, V2 >= 0, z = 1 + (1 + (1 + X36) + V2) active(z) -{ 3 }-> mark(and(isNat(X37), isNat(X40))) :|: z = 1 + (1 + (1 + X37) + (1 + X40)), X37 >= 0, X40 >= 0 active(z) -{ 3 }-> mark(and(isNat(X37), isNat(X41))) :|: X37 >= 0, X41 >= 0, z = 1 + (1 + (1 + X37) + (1 + X41)) active(z) -{ 2 }-> mark(and(isNat(X37), 0)) :|: X37 >= 0, z = 1 + (1 + (1 + X37) + V2), V2 >= 0 active(z) -{ 2 }-> mark(and(isNat(X37), 1 + V2)) :|: X37 >= 0, z = 1 + (1 + (1 + X37) + V2), V2 >= 0 active(z) -{ 2 }-> mark(and(0, isNat(X44))) :|: V1 >= 0, z = 1 + (1 + V1 + (1 + X44)), X44 >= 0 active(z) -{ 2 }-> mark(and(0, isNat(X45))) :|: z = 1 + (1 + V1 + (1 + X45)), V1 >= 0, X45 >= 0 active(z) -{ 1 }-> mark(and(0, 0)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 1 }-> mark(and(0, 1 + V2)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 2 }-> mark(and(1 + V1, isNat(X42))) :|: V1 >= 0, z = 1 + (1 + V1 + (1 + X42)), X42 >= 0 active(z) -{ 2 }-> mark(and(1 + V1, isNat(X43))) :|: z = 1 + (1 + V1 + (1 + X43)), X43 >= 0, V1 >= 0 active(z) -{ 1 }-> mark(and(1 + V1, 0)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 1 }-> mark(and(1 + V1, 1 + V2)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 3 }-> mark(U21(and(isNat(X'), isNat(X4)), 1 + X', 1 + X4)) :|: z = 1 + (1 + X4) + (1 + (1 + X')), X' >= 0, X4 >= 0 active(z) -{ 3 }-> mark(U21(and(isNat(X'), isNat(X5)), 1 + X', 1 + X5)) :|: X5 >= 0, z = 1 + (1 + X5) + (1 + (1 + X')), X' >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X'), 0), 1 + X', N)) :|: z = 1 + N + (1 + (1 + X')), X' >= 0, N >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X'), 1 + N), 1 + X', N)) :|: z = 1 + N + (1 + (1 + X')), X' >= 0, N >= 0 active(z) -{ 3 }-> mark(U21(and(isNat(X''), isNat(X6)), 1 + X'', 1 + X6)) :|: z = 1 + (1 + X6) + (1 + (1 + X'')), X6 >= 0, X'' >= 0 active(z) -{ 3 }-> mark(U21(and(isNat(X''), isNat(X7)), 1 + X'', 1 + X7)) :|: z = 1 + (1 + X7) + (1 + (1 + X'')), X7 >= 0, X'' >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X''), 0), 1 + X'', N)) :|: X'' >= 0, z = 1 + N + (1 + (1 + X'')), N >= 0 active(z) -{ 2 }-> mark(U21(and(isNat(X''), 1 + N), 1 + X'', N)) :|: X'' >= 0, z = 1 + N + (1 + (1 + X'')), N >= 0 active(z) -{ 2 }-> mark(U21(and(0, isNat(X10)), M, 1 + X10)) :|: z = 1 + (1 + X10) + (1 + M), X10 >= 0, M >= 0 active(z) -{ 2 }-> mark(U21(and(0, isNat(X11)), M, 1 + X11)) :|: X11 >= 0, z = 1 + (1 + X11) + (1 + M), M >= 0 active(z) -{ 1 }-> mark(U21(and(0, 0), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(U21(and(0, 1 + N), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 2 }-> mark(U21(and(1 + M, isNat(X8)), M, 1 + X8)) :|: X8 >= 0, M >= 0, z = 1 + (1 + X8) + (1 + M) active(z) -{ 2 }-> mark(U21(and(1 + M, isNat(X9)), M, 1 + X9)) :|: X9 >= 0, z = 1 + (1 + X9) + (1 + M), M >= 0 active(z) -{ 1 }-> mark(U21(and(1 + M, 0), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(U21(and(1 + M, 1 + N), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 2 }-> mark(U11(isNat(z - 2), 1 + (z - 2))) :|: z - 2 >= 0 active(z) -{ 1 }-> mark(U11(0, z - 1)) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(U11(1 + (z - 1), z - 1)) :|: z - 1 >= 0 active(z) -{ 1 }-> mark(1) :|: z = 1 + 0 active(z) -{ 1 }-> mark(0) :|: z - 2 >= 0 active(z) -{ 1 }-> mark(z - 2) :|: z - 2 >= 0 active(z) -{ 1 }-> mark(1 + (z - 2)) :|: z - 2 >= 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 }-> s(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(plus(encArg(x_11180), encArg(x_2589))) :|: z = 1 + (1 + x_11180 + x_2589), x_11180 >= 0, x_2589 >= 0 encArg(z) -{ 0 }-> s(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(isNat(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(and(encArg(x_11181), encArg(x_2590))) :|: z = 1 + (1 + x_11181 + x_2590), x_2590 >= 0, x_11181 >= 0 encArg(z) -{ 0 }-> s(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> s(U21(encArg(x_11178), encArg(x_2588), encArg(x_3146))) :|: x_11178 >= 0, x_3146 >= 0, x_2588 >= 0, z = 1 + (1 + x_11178 + x_2588 + x_3146) encArg(z) -{ 0 }-> s(U11(encArg(x_11177), encArg(x_2587))) :|: x_2587 >= 0, x_11177 >= 0, z = 1 + (1 + x_11177 + x_2587) 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(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(plus(encArg(x_112), encArg(x_25))) :|: x_25 >= 0, z = 1 + (1 + x_112 + x_25), x_112 >= 0 encArg(z) -{ 0 }-> mark(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(isNat(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(and(encArg(x_113), encArg(x_26))) :|: x_113 >= 0, z = 1 + (1 + x_113 + x_26), x_26 >= 0 encArg(z) -{ 0 }-> mark(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> mark(U21(encArg(x_110), encArg(x_24), encArg(x_3''))) :|: x_24 >= 0, z = 1 + (1 + x_110 + x_24 + x_3''), x_110 >= 0, x_3'' >= 0 encArg(z) -{ 0 }-> mark(U11(encArg(x_19), encArg(x_23))) :|: z = 1 + (1 + x_19 + x_23), x_23 >= 0, x_19 >= 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 }-> isNat(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> isNat(plus(encArg(x_11380), encArg(x_2689))) :|: x_11380 >= 0, z = 1 + (1 + x_11380 + x_2689), x_2689 >= 0 encArg(z) -{ 0 }-> isNat(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> isNat(isNat(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> isNat(and(encArg(x_11381), encArg(x_2690))) :|: z = 1 + (1 + x_11381 + x_2690), x_11381 >= 0, x_2690 >= 0 encArg(z) -{ 0 }-> isNat(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> isNat(U21(encArg(x_11378), encArg(x_2688), encArg(x_3171))) :|: x_3171 >= 0, z = 1 + (1 + x_11378 + x_2688 + x_3171), x_11378 >= 0, x_2688 >= 0 encArg(z) -{ 0 }-> isNat(U11(encArg(x_11377), encArg(x_2687))) :|: x_11377 >= 0, z = 1 + (1 + x_11377 + x_2687), x_2687 >= 0 encArg(z) -{ 0 }-> isNat(1) :|: z = 1 + 1 encArg(z) -{ 0 }-> isNat(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> isNat(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(s(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(plus(encArg(x_14), encArg(x_21))) :|: x_14 >= 0, z = 1 + (1 + x_14 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> active(mark(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(isNat(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(and(encArg(x_15), encArg(x_22))) :|: x_15 >= 0, z = 1 + (1 + x_15 + x_22), x_22 >= 0 encArg(z) -{ 0 }-> active(active(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> active(U21(encArg(x_12), encArg(x_2''), encArg(x_3'))) :|: x_3' >= 0, x_2'' >= 0, x_12 >= 0, z = 1 + (1 + x_12 + x_2'' + x_3') encArg(z) -{ 0 }-> active(U11(encArg(x_11), encArg(x_2'))) :|: x_11 >= 0, x_2' >= 0, z = 1 + (1 + x_11 + x_2') 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 }-> U21(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> U11(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_0 -{ 0 }-> 0 :|: encode_U11(z, z') -{ 0 }-> U11(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_U11(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_U21(z, z', z'') -{ 0 }-> U21(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0 encode_U21(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 encode_active(z) -{ 0 }-> active(s(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(plus(encArg(x_11388), encArg(x_2693))) :|: x_2693 >= 0, x_11388 >= 0, z = 1 + x_11388 + x_2693 encode_active(z) -{ 0 }-> active(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(isNat(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(and(encArg(x_11389), encArg(x_2694))) :|: x_2694 >= 0, z = 1 + x_11389 + x_2694, x_11389 >= 0 encode_active(z) -{ 0 }-> active(active(encArg(z - 1))) :|: z - 1 >= 0 encode_active(z) -{ 0 }-> active(U21(encArg(x_11386), encArg(x_2692), encArg(x_3172))) :|: x_2692 >= 0, x_11386 >= 0, z = 1 + x_11386 + x_2692 + x_3172, x_3172 >= 0 encode_active(z) -{ 0 }-> active(U11(encArg(x_11385), encArg(x_2691))) :|: x_11385 >= 0, z = 1 + x_11385 + x_2691, x_2691 >= 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_isNat(z) -{ 0 }-> isNat(s(encArg(z - 1))) :|: z - 1 >= 0 encode_isNat(z) -{ 0 }-> isNat(plus(encArg(x_12764), encArg(x_21381))) :|: x_12764 >= 0, x_21381 >= 0, z = 1 + x_12764 + x_21381 encode_isNat(z) -{ 0 }-> isNat(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_isNat(z) -{ 0 }-> isNat(isNat(encArg(z - 1))) :|: z - 1 >= 0 encode_isNat(z) -{ 0 }-> isNat(and(encArg(x_12765), encArg(x_21382))) :|: x_12765 >= 0, x_21382 >= 0, z = 1 + x_12765 + x_21382 encode_isNat(z) -{ 0 }-> isNat(active(encArg(z - 1))) :|: z - 1 >= 0 encode_isNat(z) -{ 0 }-> isNat(U21(encArg(x_12762), encArg(x_21380), encArg(x_3344))) :|: x_21380 >= 0, x_3344 >= 0, x_12762 >= 0, z = 1 + x_12762 + x_21380 + x_3344 encode_isNat(z) -{ 0 }-> isNat(U11(encArg(x_12761), encArg(x_21379))) :|: z = 1 + x_12761 + x_21379, x_12761 >= 0, x_21379 >= 0 encode_isNat(z) -{ 0 }-> isNat(1) :|: z = 1 encode_isNat(z) -{ 0 }-> isNat(0) :|: z = 0 encode_isNat(z) -{ 0 }-> isNat(0) :|: z >= 0 encode_isNat(z) -{ 0 }-> 0 :|: z >= 0 encode_mark(z) -{ 0 }-> mark(s(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(plus(encArg(x_11492), encArg(x_2745))) :|: x_11492 >= 0, z = 1 + x_11492 + x_2745, x_2745 >= 0 encode_mark(z) -{ 0 }-> mark(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(isNat(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(and(encArg(x_11493), encArg(x_2746))) :|: x_11493 >= 0, z = 1 + x_11493 + x_2746, x_2746 >= 0 encode_mark(z) -{ 0 }-> mark(active(encArg(z - 1))) :|: z - 1 >= 0 encode_mark(z) -{ 0 }-> mark(U21(encArg(x_11490), encArg(x_2744), encArg(x_3185))) :|: x_2744 >= 0, x_3185 >= 0, x_11490 >= 0, z = 1 + x_11490 + x_2744 + x_3185 encode_mark(z) -{ 0 }-> mark(U11(encArg(x_11489), encArg(x_2743))) :|: x_2743 >= 0, z = 1 + x_11489 + x_2743, x_11489 >= 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(s(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(plus(encArg(x_12564), encArg(x_21281))) :|: x_21281 >= 0, z = 1 + x_12564 + x_21281, x_12564 >= 0 encode_s(z) -{ 0 }-> s(mark(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(isNat(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(and(encArg(x_12565), encArg(x_21282))) :|: x_12565 >= 0, x_21282 >= 0, z = 1 + x_12565 + x_21282 encode_s(z) -{ 0 }-> s(active(encArg(z - 1))) :|: z - 1 >= 0 encode_s(z) -{ 0 }-> s(U21(encArg(x_12562), encArg(x_21280), encArg(x_3319))) :|: z = 1 + x_12562 + x_21280 + x_3319, x_3319 >= 0, x_12562 >= 0, x_21280 >= 0 encode_s(z) -{ 0 }-> s(U11(encArg(x_12561), encArg(x_21279))) :|: x_21279 >= 0, x_12561 >= 0, z = 1 + x_12561 + x_21279 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 :|: isNat(z) -{ 1 }-> isNat(z - 1) :|: z - 1 >= 0 isNat(z) -{ 0 }-> 0 :|: z >= 0 isNat(z) -{ 0 }-> 1 + z :|: z >= 0 mark(z) -{ 2 }-> active(s(active(s(mark(z - 2))))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(plus(mark(X17), mark(X24))))) :|: z = 1 + (1 + X17 + X24), X17 >= 0, X24 >= 0 mark(z) -{ 2 }-> active(s(active(isNat(z - 2)))) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(s(active(and(mark(X14), X22)))) :|: z = 1 + (1 + X14 + X22), X22 >= 0, X14 >= 0 mark(z) -{ 2 }-> active(s(active(U21(mark(X15), X23, X3')))) :|: X3' >= 0, X15 >= 0, X23 >= 0, z = 1 + (1 + X15 + X23 + X3') mark(z) -{ 2 }-> active(s(active(U11(mark(X13), X21)))) :|: X21 >= 0, X13 >= 0, z = 1 + (1 + X13 + X21) 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(isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(and(active(s(mark(X31))), X2)) :|: z = 1 + (1 + X31) + X2, X31 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(plus(mark(X116), mark(X213))), X2)) :|: z = 1 + (1 + X116 + X213) + X2, X213 >= 0, X116 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(isNat(X33)), X2)) :|: X33 >= 0, z = 1 + (1 + X33) + X2, X2 >= 0 mark(z) -{ 2 }-> active(and(active(and(mark(X114), X211)), X2)) :|: X114 >= 0, z = 1 + (1 + X114 + X211) + X2, X211 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(and(active(U21(mark(X115), X212, X32)), X2)) :|: X212 >= 0, X32 >= 0, X115 >= 0, X2 >= 0, z = 1 + (1 + X115 + X212 + X32) + X2 mark(z) -{ 2 }-> active(and(active(U11(mark(X113), X210)), X2)) :|: X113 >= 0, z = 1 + (1 + X113 + X210) + X2, X2 >= 0, X210 >= 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) -{ 2 }-> active(U21(active(s(mark(X46))), X2, X3)) :|: X3 >= 0, X46 >= 0, X2 >= 0, z = 1 + (1 + X46) + X2 + X3 mark(z) -{ 2 }-> active(U21(active(plus(mark(X120), mark(X217))), X2, X3)) :|: X120 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X120 + X217) + X2 + X3, X217 >= 0 mark(z) -{ 2 }-> active(U21(active(isNat(X47)), X2, X3)) :|: z = 1 + (1 + X47) + X2 + X3, X47 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(and(mark(X118), X215)), X2, X3)) :|: z = 1 + (1 + X118 + X215) + X2 + X3, X118 >= 0, X3 >= 0, X215 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(U21(mark(X119), X216, X310)), X2, X3)) :|: X216 >= 0, X3 >= 0, X310 >= 0, X2 >= 0, z = 1 + (1 + X119 + X216 + X310) + X2 + X3, X119 >= 0 mark(z) -{ 2 }-> active(U21(active(U11(mark(X117), X214)), X2, X3)) :|: X117 >= 0, X214 >= 0, X3 >= 0, z = 1 + (1 + X117 + X214) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(1), X2, X3)) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U21(active(0), X2, X3)) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 1 }-> active(U21(0, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U21(1 + X1, X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(s(mark(X18))), X2)) :|: z = 1 + (1 + X18) + X2, X18 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(plus(mark(X112), mark(X28))), X2)) :|: z = 1 + (1 + X112 + X28) + X2, X28 >= 0, X112 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(isNat(X20)), X2)) :|: z = 1 + (1 + X20) + X2, X20 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(and(mark(X110), X26)), X2)) :|: X110 >= 0, z = 1 + (1 + X110 + X26) + X2, X26 >= 0, X2 >= 0 mark(z) -{ 2 }-> active(U11(active(U21(mark(X111), X27, X3'')), X2)) :|: X27 >= 0, X3'' >= 0, z = 1 + (1 + X111 + X27 + X3'') + X2, X2 >= 0, X111 >= 0 mark(z) -{ 2 }-> active(U11(active(U11(mark(X19), X25)), X2)) :|: z = 1 + (1 + X19 + X25) + X2, X19 >= 0, X2 >= 0, X25 >= 0 mark(z) -{ 2 }-> active(U11(active(1), z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> active(U11(active(0), z - 1)) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(U11(0, X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(U11(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) -{ 1 }-> active(0) :|: z - 1 >= 0 mark(z) -{ 1 }-> active(1 + (z - 1)) :|: z - 1 >= 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 ---------------------------------------- (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_U11(v0, v1) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U21(v0, v1, v2) -> null_encode_U21 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_and(v0, v1) -> null_encode_and [0] encode_isNat(v0) -> null_encode_isNat [0] encode_0 -> null_encode_0 [0] isNat(v0) -> null_isNat [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U21(v0, v1, v2) -> null_U21 [0] and(v0, v1) -> null_and [0] U11(v0, v1) -> null_U11 [0] mark(v0) -> null_mark [0] And the following fresh constants: null_encArg, null_encode_active, null_encode_U11, null_encode_tt, null_encode_mark, null_encode_U21, null_encode_s, null_encode_plus, null_encode_and, null_encode_isNat, null_encode_0, null_isNat, null_s, null_active, null_plus, null_U21, null_and, null_U11, 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] active(c_isNat(0)) -> mark(tt) [1] U21(X1, X2, c_mark(X3)) -> U21(X1, X2, X3) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] active(c_U21(tt, M, N)) -> mark(s(plus(N, M))) [1] active(c_plus(N, c_s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) [1] U21(c_mark(X1), X2, X3) -> U21(X1, X2, X3) [1] isNat(c_active(X)) -> isNat(X) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] s(c_active(X)) -> s(X) [1] and(c_active(X1), X2) -> and(X1, X2) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] active(c_plus(N, 0)) -> mark(U11(isNat(N), N)) [1] mark(c_and(X1, X2)) -> active(and(mark(X1), X2)) [1] active(c_isNat(c_s(V1))) -> mark(isNat(V1)) [1] active(c_U11(tt, N)) -> mark(N) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U21(X1, c_mark(X2), X3) -> U21(X1, X2, X3) [1] s(c_mark(X)) -> s(X) [1] plus(c_mark(X1), X2) -> plus(X1, X2) [1] U11(c_mark(X1), X2) -> U11(X1, X2) [1] U11(X1, c_active(X2)) -> U11(X1, X2) [1] U21(X1, X2, c_active(X3)) -> U21(X1, X2, X3) [1] U21(c_active(X1), X2, X3) -> U21(X1, X2, X3) [1] active(c_and(tt, X)) -> mark(X) [1] active(c_isNat(c_plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) [1] mark(c_U21(X1, X2, X3)) -> active(U21(mark(X1), X2, X3)) [1] mark(c_isNat(X)) -> active(isNat(X)) [1] and(X1, c_mark(X2)) -> and(X1, X2) [1] and(c_mark(X1), X2) -> and(X1, X2) [1] U21(X1, c_active(X2), X3) -> U21(X1, X2, X3) [1] plus(X1, c_active(X2)) -> plus(X1, X2) [1] mark(c_plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) [1] U11(c_active(X1), X2) -> U11(X1, X2) [1] isNat(c_mark(X)) -> isNat(X) [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_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) [0] encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_s(x_1)) -> s(encArg(x_1)) [0] encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) [0] encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encode_active(x_1) -> active(encArg(x_1)) [0] encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) [0] encode_tt -> tt [0] encode_mark(x_1) -> mark(encArg(x_1)) [0] encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_s(x_1) -> s(encArg(x_1)) [0] encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) [0] encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_0 -> 0 [0] isNat(x0) -> c_isNat(x0) [0] s(x0) -> c_s(x0) [0] active(x0) -> c_active(x0) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U21(x0, x1, x2) -> c_U21(x0, x1, x2) [0] and(x0, x1) -> c_and(x0, x1) [0] U11(x0, x1) -> c_U11(x0, x1) [0] mark(x0) -> c_mark(x0) [0] encArg(v0) -> null_encArg [0] encode_active(v0) -> null_encode_active [0] encode_U11(v0, v1) -> null_encode_U11 [0] encode_tt -> null_encode_tt [0] encode_mark(v0) -> null_encode_mark [0] encode_U21(v0, v1, v2) -> null_encode_U21 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_and(v0, v1) -> null_encode_and [0] encode_isNat(v0) -> null_encode_isNat [0] encode_0 -> null_encode_0 [0] isNat(v0) -> null_isNat [0] s(v0) -> null_s [0] active(v0) -> null_active [0] plus(v0, v1) -> null_plus [0] U21(v0, v1, v2) -> null_U21 [0] and(v0, v1) -> null_and [0] U11(v0, v1) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark 0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark c_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encArg :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark cons_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark -> tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark encode_0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encArg :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_tt :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_encode_0 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_isNat :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_s :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_active :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_plus :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_U21 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_and :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_U11 :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11:null_mark null_mark :: tt:0:c_isNat:c_mark:c_U21:c_s:c_plus:c_active:c_U11:c_and:cons_active:cons_mark:cons_U11:cons_U21:cons_s:cons_plus:cons_and:cons_isNat:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U21:null_encode_s:null_encode_plus:null_encode_and:null_encode_isNat:null_encode_0:null_isNat:null_s:null_active:null_plus:null_U21:null_and:null_U11: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_U11 => 0 null_encode_tt => 0 null_encode_mark => 0 null_encode_U21 => 0 null_encode_s => 0 null_encode_plus => 0 null_encode_and => 0 null_encode_isNat => 0 null_encode_0 => 0 null_isNat => 0 null_s => 0 null_active => 0 null_plus => 0 null_U21 => 0 null_and => 0 null_U11 => 0 null_mark => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: U11(z, z') -{ 1 }-> U11(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 U11(z, z') -{ 1 }-> U11(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 U11(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 U21(z, z', z'') -{ 1 }-> U21(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U21(z, z', z'') -{ 1 }-> U21(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U21(z, z', z'') -{ 1 }-> U21(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U21(z, z', z'') -{ 0 }-> 1 + x0 + x1 + x2 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1, z'' = x2, x2 >= 0 active(z) -{ 1 }-> mark(N) :|: z = 1 + 1 + N, N >= 0 active(z) -{ 1 }-> mark(X) :|: z = 1 + 1 + X, X >= 0 active(z) -{ 1 }-> mark(s(plus(N, M))) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(isNat(V1)) :|: V1 >= 0, z = 1 + (1 + V1) active(z) -{ 1 }-> mark(and(isNat(V1), isNat(V2))) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 1 }-> mark(U21(and(isNat(M), isNat(N)), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(U11(isNat(N), N)) :|: z = 1 + N + 0, N >= 0 active(z) -{ 1 }-> mark(1) :|: z = 1 + 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 }-> 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 }-> isNat(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 }-> U21(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encArg(z) -{ 0 }-> U11(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 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_U11(z, z') -{ 0 }-> U11(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_U21(z, z', z'') -{ 0 }-> U21(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 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_isNat(z) -{ 0 }-> isNat(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_mark(z) -{ 0 }-> mark(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_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 :|: isNat(z) -{ 1 }-> isNat(X) :|: z = 1 + X, X >= 0 isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 isNat(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 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(isNat(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(and(mark(X1), X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(U21(mark(X1), X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U11(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 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encode_active(z0) -> active(encArg(z0)) encode_U11(z0, z1) -> U11(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U21(z0, z1, z2) -> U21(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_isNat(z0) -> isNat(encArg(z0)) encode_0 -> 0 active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) 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_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ENCODE_ACTIVE(z0) -> c10(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1) -> c11(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_TT -> c12 ENCODE_MARK(z0) -> c13(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U21(z0, z1, z2) -> c14(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c15(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c16(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_AND(z0, z1) -> c17(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ISNAT(z0) -> c18(ISNAT(encArg(z0)), ENCARG(z0)) ENCODE_0 -> c19 ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), U11'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), U21'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c29(ACTIVE(tt)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(0) -> c35(ACTIVE(0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), U11'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), U21'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c29(ACTIVE(tt)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(0) -> c35(ACTIVE(0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U21_3, encode_s_1, encode_plus_2, encode_and_2, encode_isNat_1, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_TT, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCODE_0, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1 Compound Symbols: c, c1, c2_2, c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c10_2, c11_3, c12, c13_2, c14_4, c15_2, c16_3, c17_3, c18_2, c19, c20_1, c21_3, c22_1, c23_1, c24_4, c25_2, c26_3, c27_5, c28_3, c29_1, c30_3, c31_3, c32_4, c33_3, c34_2, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: ENCARG(tt) -> c ENCODE_TT -> c12 ENCODE_0 -> c19 ENCARG(0) -> c1 ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encode_active(z0) -> active(encArg(z0)) encode_U11(z0, z1) -> U11(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U21(z0, z1, z2) -> U21(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_isNat(z0) -> isNat(encArg(z0)) encode_0 -> 0 active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ENCODE_ACTIVE(z0) -> c10(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1) -> c11(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MARK(z0) -> c13(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U21(z0, z1, z2) -> c14(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c15(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c16(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_AND(z0, z1) -> c17(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ISNAT(z0) -> c18(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), U11'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), U21'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c29(ACTIVE(tt)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(0) -> c35(ACTIVE(0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), AND(isNat(z0), isNat(z1)), ISNAT(z0), ISNAT(z1)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), U11'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), U21'(and(isNat(z1), isNat(z0)), z1, z0), AND(isNat(z1), isNat(z0)), ISNAT(z1), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c29(ACTIVE(tt)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(0) -> c35(ACTIVE(0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U21_3, encode_s_1, encode_plus_2, encode_and_2, encode_isNat_1, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1 Compound Symbols: c2_2, c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c10_2, c11_3, c13_2, c14_4, c15_2, c16_3, c17_3, c18_2, c20_1, c21_3, c22_1, c23_1, c24_4, c25_2, c26_3, c27_5, c28_3, c29_1, c30_3, c31_3, c32_4, c33_3, c34_2, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encode_active(z0) -> active(encArg(z0)) encode_U11(z0, z1) -> U11(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U21(z0, z1, z2) -> U21(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_isNat(z0) -> isNat(encArg(z0)) encode_0 -> 0 active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ENCODE_ACTIVE(z0) -> c10(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1) -> c11(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MARK(z0) -> c13(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U21(z0, z1, z2) -> c14(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c15(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c16(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_AND(z0, z1) -> c17(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ISNAT(z0) -> c18(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U21_3, encode_s_1, encode_plus_2, encode_and_2, encode_isNat_1, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1 Compound Symbols: c2_2, c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c10_2, c11_3, c13_2, c14_4, c15_2, c16_3, c17_3, c18_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35 ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encode_active(z0) -> active(encArg(z0)) encode_U11(z0, z1) -> U11(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U21(z0, z1, z2) -> U21(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_isNat(z0) -> isNat(encArg(z0)) encode_0 -> 0 active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_U11(z0, z1) -> c(ENCARG(z0)) ENCODE_U11(z0, z1) -> c(ENCARG(z1)) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U21(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U21(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U21(z0, z1, z2) -> c(ENCARG(z2)) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_S(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_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(ENCARG(z0)) ENCODE_AND(z0, z1) -> c(ENCARG(z1)) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_ISNAT(z0) -> c(ENCARG(z0)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U21_3, encode_s_1, encode_plus_2, encode_and_2, encode_isNat_1, encode_0 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c2_2, c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1 ---------------------------------------- (43) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 13 leading nodes: ENCODE_ACTIVE(z0) -> c(ENCARG(z0)) ENCODE_U11(z0, z1) -> c(ENCARG(z0)) ENCODE_U11(z0, z1) -> c(ENCARG(z1)) ENCODE_MARK(z0) -> c(ENCARG(z0)) ENCODE_U21(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U21(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U21(z0, z1, z2) -> c(ENCARG(z2)) ENCODE_S(z0) -> c(ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c(ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c(ENCARG(z1)) ENCODE_AND(z0, z1) -> c(ENCARG(z0)) ENCODE_AND(z0, z1) -> c(ENCARG(z1)) ENCODE_ISNAT(z0) -> c(ENCARG(z0)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encode_active(z0) -> active(encArg(z0)) encode_U11(z0, z1) -> U11(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U21(z0, z1, z2) -> U21(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_isNat(z0) -> isNat(encArg(z0)) encode_0 -> 0 active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U21_3, encode_s_1, encode_plus_2, encode_and_2, encode_isNat_1, encode_0 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c2_2, c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1 ---------------------------------------- (45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_active(z0) -> active(encArg(z0)) encode_U11(z0, z1) -> U11(encArg(z0), encArg(z1)) encode_tt -> tt encode_mark(z0) -> mark(encArg(z0)) encode_U21(z0, z1, z2) -> U21(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_and(z0, z1) -> and(encArg(z0), encArg(z1)) encode_isNat(z0) -> isNat(encArg(z0)) encode_0 -> 0 ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_active(z0)) -> c2(ACTIVE(encArg(z0)), ENCARG(z0)) ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c2_2, c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2 ---------------------------------------- (49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ENCARG(cons_active(tt)) -> c2(ACTIVE(tt), ENCARG(tt)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_mark(z0)) -> c3(MARK(encArg(z0)), ENCARG(z0)) ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c3_2, c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, 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_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) 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_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c4_3, c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c5_4, c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U21(z0, z1, z2)) -> c5(U21'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) by ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_s(z0)) -> c6(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c6_2, c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3 ---------------------------------------- (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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_s(0)) -> c6(S(0), ENCARG(0)) ENCARG(cons_s(tt)) -> c6(S(tt), ENCARG(tt)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c7_3, c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_plus(z0, z1)) -> c7(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c8_3, c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_and(z0, z1)) -> c8(AND(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c9_2, c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_isNat(z0)) -> c9(ISNAT(encArg(z0)), ENCARG(z0)) by ENCARG(cons_isNat(tt)) -> c9(ISNAT(tt), ENCARG(tt)) ENCARG(cons_isNat(0)) -> c9(ISNAT(0), ENCARG(0)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(tt)) -> c9(ISNAT(tt), ENCARG(tt)) ENCARG(cons_isNat(0)) -> c9(ISNAT(0), ENCARG(0)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_isNat(0)) -> c9(ISNAT(0), ENCARG(0)) ENCARG(cons_isNat(tt)) -> c9(ISNAT(tt), ENCARG(tt)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c28_3, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c28(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) by MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c30_3, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) by MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c31_3, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(s(z0)) -> c31(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) by MARK(s(z0)) -> c31(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(z0)) -> c31(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(z0)) -> c31(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c32_4, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c32(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c33_3, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c33(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0)) by MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ACTIVE(z0) -> c(ACTIVE(encArg(z0))) ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (91) 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_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), 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_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) by ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (97) 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (99) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_MARK(tt) -> c(MARK(tt)) ENCODE_MARK(0) -> c(MARK(0)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U21(z0, z1, z2) -> c(U21'(encArg(z0), encArg(z1), encArg(z2))) by ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (103) 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_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) 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_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_S(tt) -> c(S(tt)) ENCODE_S(0) -> c(S(0)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (107) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_AND(z0, z1) -> c(AND(encArg(z0), encArg(z1))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_AND_2, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (109) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCODE_ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) by ENCODE_ISNAT(tt) -> c(ISNAT(tt)) ENCODE_ISNAT(0) -> c(ISNAT(0)) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(tt) -> c(ISNAT(tt)) ENCODE_ISNAT(0) -> c(ISNAT(0)) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_ISNAT(0) -> c(ISNAT(0)) ENCODE_ISNAT(tt) -> c(ISNAT(tt)) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 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_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1 ---------------------------------------- (115) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1 ---------------------------------------- (117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt)), ENCARG(cons_active(tt))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1 ---------------------------------------- (119) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1 ---------------------------------------- (121) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c1_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) by ENCARG(cons_active(cons_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c1_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_U21(z0, z1, z2))) -> c2(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) by ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_s(z0))) -> c2(ACTIVE(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c1_1 ---------------------------------------- (127) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c1_1 ---------------------------------------- (129) 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))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_plus(z0, z1))) -> c2(ACTIVE(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c1_1 ---------------------------------------- (131) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_and(z0, z1))) -> c2(ACTIVE(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c1_1 ---------------------------------------- (133) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_active(z0))) -> c3(MARK(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c2_2, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c1_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) by ENCARG(cons_active(cons_isNat(tt))) -> c2(ACTIVE(isNat(tt)), ENCARG(cons_isNat(tt))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(0)), ENCARG(cons_isNat(0))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 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_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(tt))) -> c2(ACTIVE(isNat(tt)), ENCARG(cons_isNat(tt))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(0)), ENCARG(cons_isNat(0))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1 ---------------------------------------- (137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCARG(cons_active(cons_isNat(tt))) -> c2(ACTIVE(isNat(tt)), ENCARG(cons_isNat(tt))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 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_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(0)), ENCARG(cons_isNat(0))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 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_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1 ---------------------------------------- (141) 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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(0))) 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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1 ---------------------------------------- (143) 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))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_mark(z0))) -> c3(MARK(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1 ---------------------------------------- (145) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1 ---------------------------------------- (147) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, cons_U11(z0, z1))) -> c4(U11'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) by ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, cons_U21(z0, z1, z2))) -> c4(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) by ENCARG(cons_U11(x0, cons_U21(x1, x2, tt))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), tt)), ENCARG(x0), ENCARG(cons_U21(x1, x2, tt))) ENCARG(cons_U11(x0, cons_U21(x1, x2, 0))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), 0)), ENCARG(x0), ENCARG(cons_U21(x1, x2, 0))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_active(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_mark(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_s(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, tt, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), tt, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, tt, x3))) ENCARG(cons_U11(x0, cons_U21(x1, 0, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), 0, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, 0, x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_active(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), active(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_active(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_mark(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), mark(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_mark(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U11(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U11(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U11(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U21(z0, z1, z2), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U21(z0, z1, z2), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_s(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), s(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_s(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_plus(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), plus(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_plus(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_and(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), and(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_and(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_isNat(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), isNat(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_isNat(z0), x3))) ENCARG(cons_U11(x0, cons_U21(tt, x2, x3))) -> c4(U11'(encArg(x0), U21(tt, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(tt, x2, x3))) ENCARG(cons_U11(x0, cons_U21(0, x2, x3))) -> c4(U11'(encArg(x0), U21(0, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(0, x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_active(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(active(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_active(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_mark(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(mark(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_mark(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U11(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(U11(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U11(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U21(z0, z1, z2), x2, x3))) -> c4(U11'(encArg(x0), U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U21(z0, z1, z2), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_s(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(s(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_s(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_plus(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(plus(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_plus(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_and(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(and(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_and(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_isNat(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(isNat(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_isNat(z0), x2, x3))) ENCARG(cons_U11(tt, cons_U21(x1, x2, x3))) -> c4(U11'(tt, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(tt), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(0, cons_U21(x1, x2, x3))) -> c4(U11'(0, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(0), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_active(z0), cons_U21(x1, x2, x3))) -> c4(U11'(active(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_active(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_mark(z0), cons_U21(x1, x2, x3))) -> c4(U11'(mark(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_mark(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U21(x1, x2, x3))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_s(z0), cons_U21(x1, x2, x3))) -> c4(U11'(s(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_s(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_and(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(and(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_isNat(z0), cons_U21(x1, x2, x3))) -> c4(U11'(isNat(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_isNat(z0)), ENCARG(cons_U21(x1, x2, x3))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(x0, cons_U21(x1, x2, tt))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), tt)), ENCARG(x0), ENCARG(cons_U21(x1, x2, tt))) ENCARG(cons_U11(x0, cons_U21(x1, x2, 0))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), 0)), ENCARG(x0), ENCARG(cons_U21(x1, x2, 0))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_active(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_mark(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_s(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, tt, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), tt, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, tt, x3))) ENCARG(cons_U11(x0, cons_U21(x1, 0, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), 0, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, 0, x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_active(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), active(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_active(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_mark(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), mark(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_mark(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U11(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U11(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U11(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U21(z0, z1, z2), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U21(z0, z1, z2), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_s(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), s(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_s(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_plus(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), plus(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_plus(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_and(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), and(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_and(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_isNat(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), isNat(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_isNat(z0), x3))) ENCARG(cons_U11(x0, cons_U21(tt, x2, x3))) -> c4(U11'(encArg(x0), U21(tt, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(tt, x2, x3))) ENCARG(cons_U11(x0, cons_U21(0, x2, x3))) -> c4(U11'(encArg(x0), U21(0, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(0, x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_active(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(active(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_active(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_mark(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(mark(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_mark(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U11(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(U11(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U11(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U21(z0, z1, z2), x2, x3))) -> c4(U11'(encArg(x0), U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U21(z0, z1, z2), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_s(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(s(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_s(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_plus(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(plus(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_plus(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_and(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(and(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_and(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_isNat(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(isNat(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_isNat(z0), x2, x3))) ENCARG(cons_U11(tt, cons_U21(x1, x2, x3))) -> c4(U11'(tt, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(tt), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(0, cons_U21(x1, x2, x3))) -> c4(U11'(0, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(0), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_active(z0), cons_U21(x1, x2, x3))) -> c4(U11'(active(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_active(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_mark(z0), cons_U21(x1, x2, x3))) -> c4(U11'(mark(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_mark(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U21(x1, x2, x3))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_s(z0), cons_U21(x1, x2, x3))) -> c4(U11'(s(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_s(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_and(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(and(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_isNat(z0), cons_U21(x1, x2, x3))) -> c4(U11'(isNat(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_isNat(z0)), ENCARG(cons_U21(x1, x2, x3))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(x0, cons_U21(x1, x2, tt))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), tt)), ENCARG(x0), ENCARG(cons_U21(x1, x2, tt))) ENCARG(cons_U11(x0, cons_U21(x1, x2, 0))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), 0)), ENCARG(x0), ENCARG(cons_U21(x1, x2, 0))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_active(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_mark(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_s(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, tt, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), tt, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, tt, x3))) ENCARG(cons_U11(x0, cons_U21(x1, 0, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), 0, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, 0, x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_active(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), active(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_active(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_mark(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), mark(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_mark(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U11(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U11(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U11(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U21(z0, z1, z2), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U21(z0, z1, z2), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_s(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), s(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_s(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_plus(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), plus(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_plus(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_and(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), and(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_and(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_isNat(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), isNat(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_isNat(z0), x3))) ENCARG(cons_U11(x0, cons_U21(tt, x2, x3))) -> c4(U11'(encArg(x0), U21(tt, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(tt, x2, x3))) ENCARG(cons_U11(x0, cons_U21(0, x2, x3))) -> c4(U11'(encArg(x0), U21(0, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(0, x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_active(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(active(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_active(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_mark(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(mark(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_mark(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U11(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(U11(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U11(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U21(z0, z1, z2), x2, x3))) -> c4(U11'(encArg(x0), U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U21(z0, z1, z2), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_s(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(s(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_s(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_plus(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(plus(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_plus(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_and(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(and(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_and(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_isNat(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(isNat(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_isNat(z0), x2, x3))) ENCARG(cons_U11(cons_active(z0), cons_U21(x1, x2, x3))) -> c4(U11'(active(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_active(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_mark(z0), cons_U21(x1, x2, x3))) -> c4(U11'(mark(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_mark(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U21(x1, x2, x3))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_s(z0), cons_U21(x1, x2, x3))) -> c4(U11'(s(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_s(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_and(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(and(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_isNat(z0), cons_U21(x1, x2, x3))) -> c4(U11'(isNat(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_isNat(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(tt, cons_U21(x1, x2, x3))) -> c4(U11'(tt, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(0, cons_U21(x1, x2, x3))) -> c4(U11'(0, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, cons_s(z0))) -> c4(U11'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) by ENCARG(cons_U11(x0, cons_s(tt))) -> c4(U11'(encArg(x0), s(tt)), ENCARG(x0), ENCARG(cons_s(tt))) ENCARG(cons_U11(x0, cons_s(0))) -> c4(U11'(encArg(x0), s(0)), ENCARG(x0), ENCARG(cons_s(0))) ENCARG(cons_U11(x0, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, cons_s(cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), s(U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_s(cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_and(z0, z1)))) -> c4(U11'(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_isNat(z0)))) -> c4(U11'(encArg(x0), s(isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_isNat(z0)))) ENCARG(cons_U11(tt, cons_s(x1))) -> c4(U11'(tt, s(encArg(x1))), ENCARG(tt), ENCARG(cons_s(x1))) ENCARG(cons_U11(0, cons_s(x1))) -> c4(U11'(0, s(encArg(x1))), ENCARG(0), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_active(z0), cons_s(x1))) -> c4(U11'(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_mark(z0), cons_s(x1))) -> c4(U11'(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U11(z0, z1), cons_s(x1))) -> c4(U11'(U11(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_s(x1))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x1))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_s(z0), cons_s(x1))) -> c4(U11'(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_plus(z0, z1), cons_s(x1))) -> c4(U11'(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_and(z0, z1), cons_s(x1))) -> c4(U11'(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_isNat(z0), cons_s(x1))) -> c4(U11'(isNat(encArg(z0)), s(encArg(x1))), ENCARG(cons_isNat(z0)), ENCARG(cons_s(x1))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(x0, cons_U21(x1, x2, tt))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), tt)), ENCARG(x0), ENCARG(cons_U21(x1, x2, tt))) ENCARG(cons_U11(x0, cons_U21(x1, x2, 0))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), 0)), ENCARG(x0), ENCARG(cons_U21(x1, x2, 0))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_active(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_mark(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_s(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, tt, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), tt, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, tt, x3))) ENCARG(cons_U11(x0, cons_U21(x1, 0, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), 0, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, 0, x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_active(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), active(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_active(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_mark(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), mark(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_mark(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U11(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U11(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U11(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U21(z0, z1, z2), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U21(z0, z1, z2), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_s(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), s(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_s(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_plus(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), plus(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_plus(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_and(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), and(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_and(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_isNat(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), isNat(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_isNat(z0), x3))) ENCARG(cons_U11(x0, cons_U21(tt, x2, x3))) -> c4(U11'(encArg(x0), U21(tt, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(tt, x2, x3))) ENCARG(cons_U11(x0, cons_U21(0, x2, x3))) -> c4(U11'(encArg(x0), U21(0, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(0, x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_active(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(active(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_active(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_mark(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(mark(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_mark(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U11(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(U11(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U11(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U21(z0, z1, z2), x2, x3))) -> c4(U11'(encArg(x0), U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U21(z0, z1, z2), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_s(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(s(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_s(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_plus(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(plus(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_plus(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_and(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(and(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_and(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_isNat(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(isNat(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_isNat(z0), x2, x3))) ENCARG(cons_U11(cons_active(z0), cons_U21(x1, x2, x3))) -> c4(U11'(active(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_active(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_mark(z0), cons_U21(x1, x2, x3))) -> c4(U11'(mark(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_mark(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U21(x1, x2, x3))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_s(z0), cons_U21(x1, x2, x3))) -> c4(U11'(s(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_s(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_and(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(and(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_isNat(z0), cons_U21(x1, x2, x3))) -> c4(U11'(isNat(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_isNat(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(tt, cons_U21(x1, x2, x3))) -> c4(U11'(tt, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(0, cons_U21(x1, x2, x3))) -> c4(U11'(0, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(x0, cons_s(tt))) -> c4(U11'(encArg(x0), s(tt)), ENCARG(x0), ENCARG(cons_s(tt))) ENCARG(cons_U11(x0, cons_s(0))) -> c4(U11'(encArg(x0), s(0)), ENCARG(x0), ENCARG(cons_s(0))) ENCARG(cons_U11(x0, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, cons_s(cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), s(U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_s(cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_and(z0, z1)))) -> c4(U11'(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_isNat(z0)))) -> c4(U11'(encArg(x0), s(isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_isNat(z0)))) ENCARG(cons_U11(tt, cons_s(x1))) -> c4(U11'(tt, s(encArg(x1))), ENCARG(tt), ENCARG(cons_s(x1))) ENCARG(cons_U11(0, cons_s(x1))) -> c4(U11'(0, s(encArg(x1))), ENCARG(0), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_active(z0), cons_s(x1))) -> c4(U11'(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_mark(z0), cons_s(x1))) -> c4(U11'(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U11(z0, z1), cons_s(x1))) -> c4(U11'(U11(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_s(x1))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x1))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_s(z0), cons_s(x1))) -> c4(U11'(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_plus(z0, z1), cons_s(x1))) -> c4(U11'(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_and(z0, z1), cons_s(x1))) -> c4(U11'(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_isNat(z0), cons_s(x1))) -> c4(U11'(isNat(encArg(z0)), s(encArg(x1))), ENCARG(cons_isNat(z0)), ENCARG(cons_s(x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(x0, cons_U21(x1, x2, tt))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), tt)), ENCARG(x0), ENCARG(cons_U21(x1, x2, tt))) ENCARG(cons_U11(x0, cons_U21(x1, x2, 0))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), 0)), ENCARG(x0), ENCARG(cons_U21(x1, x2, 0))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_active(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_mark(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_s(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, tt, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), tt, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, tt, x3))) ENCARG(cons_U11(x0, cons_U21(x1, 0, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), 0, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, 0, x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_active(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), active(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_active(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_mark(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), mark(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_mark(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U11(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U11(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U11(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U21(z0, z1, z2), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U21(z0, z1, z2), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_s(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), s(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_s(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_plus(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), plus(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_plus(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_and(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), and(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_and(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_isNat(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), isNat(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_isNat(z0), x3))) ENCARG(cons_U11(x0, cons_U21(tt, x2, x3))) -> c4(U11'(encArg(x0), U21(tt, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(tt, x2, x3))) ENCARG(cons_U11(x0, cons_U21(0, x2, x3))) -> c4(U11'(encArg(x0), U21(0, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(0, x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_active(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(active(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_active(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_mark(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(mark(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_mark(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U11(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(U11(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U11(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U21(z0, z1, z2), x2, x3))) -> c4(U11'(encArg(x0), U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U21(z0, z1, z2), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_s(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(s(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_s(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_plus(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(plus(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_plus(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_and(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(and(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_and(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_isNat(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(isNat(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_isNat(z0), x2, x3))) ENCARG(cons_U11(cons_active(z0), cons_U21(x1, x2, x3))) -> c4(U11'(active(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_active(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_mark(z0), cons_U21(x1, x2, x3))) -> c4(U11'(mark(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_mark(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U21(x1, x2, x3))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_s(z0), cons_U21(x1, x2, x3))) -> c4(U11'(s(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_s(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_and(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(and(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_isNat(z0), cons_U21(x1, x2, x3))) -> c4(U11'(isNat(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_isNat(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(tt, cons_U21(x1, x2, x3))) -> c4(U11'(tt, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(0, cons_U21(x1, x2, x3))) -> c4(U11'(0, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(x0, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, cons_s(cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), s(U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_s(cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_and(z0, z1)))) -> c4(U11'(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_isNat(z0)))) -> c4(U11'(encArg(x0), s(isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_isNat(z0)))) ENCARG(cons_U11(cons_active(z0), cons_s(x1))) -> c4(U11'(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_mark(z0), cons_s(x1))) -> c4(U11'(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U11(z0, z1), cons_s(x1))) -> c4(U11'(U11(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_s(x1))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x1))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_s(z0), cons_s(x1))) -> c4(U11'(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_plus(z0, z1), cons_s(x1))) -> c4(U11'(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_and(z0, z1), cons_s(x1))) -> c4(U11'(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_isNat(z0), cons_s(x1))) -> c4(U11'(isNat(encArg(z0)), s(encArg(x1))), ENCARG(cons_isNat(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(x0, cons_s(tt))) -> c4(U11'(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_U11(x0, cons_s(0))) -> c4(U11'(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_U11(tt, cons_s(x1))) -> c4(U11'(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_U11(0, cons_s(x1))) -> c4(U11'(0, s(encArg(x1))), ENCARG(cons_s(x1))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U11(x0, cons_plus(z0, z1))) -> c4(U11'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) by ENCARG(cons_U11(x0, cons_plus(x1, tt))) -> c4(U11'(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_U11(x0, cons_plus(x1, 0))) -> c4(U11'(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_U11(x0, cons_plus(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), plus(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_plus(tt, x2))) -> c4(U11'(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_U11(x0, cons_plus(0, x2))) -> c4(U11'(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_U11(x0, cons_plus(cons_active(z0), x2))) -> c4(U11'(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_plus(cons_s(z0), x2))) -> c4(U11'(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), plus(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_isNat(z0), x2))) ENCARG(cons_U11(tt, cons_plus(x1, x2))) -> c4(U11'(tt, plus(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(0, cons_plus(x1, x2))) -> c4(U11'(0, plus(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_active(z0), cons_plus(x1, x2))) -> c4(U11'(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_plus(x1, x2))) -> c4(U11'(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_plus(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_plus(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), plus(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_plus(x1, x2))) -> c4(U11'(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_plus(x1, x2))) -> c4(U11'(isNat(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_plus(x1, x2))) ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(x0, cons_U21(x1, x2, tt))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), tt)), ENCARG(x0), ENCARG(cons_U21(x1, x2, tt))) ENCARG(cons_U11(x0, cons_U21(x1, x2, 0))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), 0)), ENCARG(x0), ENCARG(cons_U21(x1, x2, 0))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_active(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_mark(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_s(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, tt, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), tt, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, tt, x3))) ENCARG(cons_U11(x0, cons_U21(x1, 0, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), 0, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, 0, x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_active(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), active(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_active(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_mark(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), mark(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_mark(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U11(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U11(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U11(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U21(z0, z1, z2), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U21(z0, z1, z2), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_s(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), s(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_s(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_plus(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), plus(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_plus(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_and(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), and(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_and(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_isNat(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), isNat(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_isNat(z0), x3))) ENCARG(cons_U11(x0, cons_U21(tt, x2, x3))) -> c4(U11'(encArg(x0), U21(tt, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(tt, x2, x3))) ENCARG(cons_U11(x0, cons_U21(0, x2, x3))) -> c4(U11'(encArg(x0), U21(0, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(0, x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_active(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(active(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_active(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_mark(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(mark(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_mark(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U11(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(U11(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U11(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U21(z0, z1, z2), x2, x3))) -> c4(U11'(encArg(x0), U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U21(z0, z1, z2), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_s(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(s(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_s(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_plus(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(plus(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_plus(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_and(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(and(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_and(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_isNat(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(isNat(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_isNat(z0), x2, x3))) ENCARG(cons_U11(cons_active(z0), cons_U21(x1, x2, x3))) -> c4(U11'(active(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_active(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_mark(z0), cons_U21(x1, x2, x3))) -> c4(U11'(mark(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_mark(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U21(x1, x2, x3))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_s(z0), cons_U21(x1, x2, x3))) -> c4(U11'(s(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_s(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_and(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(and(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_isNat(z0), cons_U21(x1, x2, x3))) -> c4(U11'(isNat(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_isNat(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(tt, cons_U21(x1, x2, x3))) -> c4(U11'(tt, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(0, cons_U21(x1, x2, x3))) -> c4(U11'(0, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(x0, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, cons_s(cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), s(U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_s(cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_and(z0, z1)))) -> c4(U11'(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_isNat(z0)))) -> c4(U11'(encArg(x0), s(isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_isNat(z0)))) ENCARG(cons_U11(cons_active(z0), cons_s(x1))) -> c4(U11'(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_mark(z0), cons_s(x1))) -> c4(U11'(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U11(z0, z1), cons_s(x1))) -> c4(U11'(U11(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_s(x1))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x1))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_s(z0), cons_s(x1))) -> c4(U11'(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_plus(z0, z1), cons_s(x1))) -> c4(U11'(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_and(z0, z1), cons_s(x1))) -> c4(U11'(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_isNat(z0), cons_s(x1))) -> c4(U11'(isNat(encArg(z0)), s(encArg(x1))), ENCARG(cons_isNat(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(x0, cons_s(tt))) -> c4(U11'(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_U11(x0, cons_s(0))) -> c4(U11'(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_U11(tt, cons_s(x1))) -> c4(U11'(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_U11(0, cons_s(x1))) -> c4(U11'(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_U11(x0, cons_plus(x1, tt))) -> c4(U11'(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_U11(x0, cons_plus(x1, 0))) -> c4(U11'(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_U11(x0, cons_plus(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), plus(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_plus(tt, x2))) -> c4(U11'(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_U11(x0, cons_plus(0, x2))) -> c4(U11'(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_U11(x0, cons_plus(cons_active(z0), x2))) -> c4(U11'(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_plus(cons_s(z0), x2))) -> c4(U11'(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), plus(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_isNat(z0), x2))) ENCARG(cons_U11(tt, cons_plus(x1, x2))) -> c4(U11'(tt, plus(encArg(x1), encArg(x2))), ENCARG(tt), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(0, cons_plus(x1, x2))) -> c4(U11'(0, plus(encArg(x1), encArg(x2))), ENCARG(0), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_active(z0), cons_plus(x1, x2))) -> c4(U11'(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_plus(x1, x2))) -> c4(U11'(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_plus(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_plus(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), plus(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_plus(x1, x2))) -> c4(U11'(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_plus(x1, x2))) -> c4(U11'(isNat(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_plus(x1, x2))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U21(z0, z1, z2)) -> U21(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) encArg(cons_and(z0, z1)) -> and(encArg(z0), encArg(z1)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) active(U11(tt, z0)) -> mark(z0) active(U21(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(and(tt, z0)) -> mark(z0) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(and(isNat(z0), isNat(z1))) active(isNat(s(z0))) -> mark(isNat(z0)) active(plus(z0, 0)) -> mark(U11(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U21(and(isNat(z1), isNat(z0)), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U21(z0, z1, z2)) -> active(U21(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) mark(and(z0, z1)) -> active(and(mark(z0), z1)) mark(isNat(z0)) -> active(isNat(z0)) mark(0) -> active(0) U11(mark(z0), z1) -> U11(z0, z1) U11(z0, mark(z1)) -> U11(z0, z1) U11(active(z0), z1) -> U11(z0, z1) U11(z0, active(z1)) -> U11(z0, z1) U21(mark(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, mark(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, mark(z2)) -> U21(z0, z1, z2) U21(active(z0), z1, z2) -> U21(z0, z1, z2) U21(z0, active(z1), z2) -> U21(z0, z1, z2) U21(z0, z1, active(z2)) -> U21(z0, z1, z2) s(mark(z0)) -> s(z0) s(active(z0)) -> s(z0) 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) 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) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) Tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 ENCARG(cons_mark(cons_U11(z0, z1))) -> c3(MARK(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_mark(cons_U21(z0, z1, z2))) -> c3(MARK(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_mark(cons_s(z0))) -> c3(MARK(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_mark(cons_plus(z0, z1))) -> c3(MARK(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_mark(cons_and(z0, z1))) -> c3(MARK(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) ENCARG(cons_U11(x0, cons_active(z0))) -> c4(U11'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U11(x0, cons_mark(z0))) -> c4(U11'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U11(x0, cons_and(z0, z1))) -> c4(U11'(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(cons_active(z0), x1)) -> c4(U11'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_mark(z0), x1)) -> c4(U11'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U11(z0, z1), x1)) -> c4(U11'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U21(z0, z1, z2), x1)) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_s(z0), x1)) -> c4(U11'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_plus(z0, z1), x1)) -> c4(U11'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_and(z0, z1), x1)) -> c4(U11'(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_isNat(z0), x1)) -> c4(U11'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U11(x0, tt)) -> c4(U11'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U11(x0, 0)) -> c4(U11'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U11(tt, x1)) -> c4(U11'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U11(0, x1)) -> c4(U11'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U21(x0, x1, cons_active(z0))) -> c5(U21'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U21(x0, x1, cons_mark(z0))) -> c5(U21'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U21(x0, x1, cons_U11(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2))) -> c5(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_U21(x0, x1, cons_s(z0))) -> c5(U21'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U21(x0, x1, cons_plus(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(x0, x1, cons_and(z0, z1))) -> c5(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_and(z0, z1))) ENCARG(cons_U21(x0, x1, cons_isNat(z0))) -> c5(U21'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(x0, cons_active(z0), x2)) -> c5(U21'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_mark(z0), x2)) -> c5(U21'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U11(z0, z1), x2)) -> c5(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2)) -> c5(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_s(z0), x2)) -> c5(U21'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_plus(z0, z1), x2)) -> c5(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_and(z0, z1), x2)) -> c5(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_and(z0, z1)), ENCARG(x2)) ENCARG(cons_U21(x0, cons_isNat(z0), x2)) -> c5(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U21(cons_active(z0), x1, x2)) -> c5(U21'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_mark(z0), x1, x2)) -> c5(U21'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U11(z0, z1), x1, x2)) -> c5(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2)) -> c5(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_s(z0), x1, x2)) -> c5(U21'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_plus(z0, z1), x1, x2)) -> c5(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_and(z0, z1), x1, x2)) -> c5(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_and(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(cons_isNat(z0), x1, x2)) -> c5(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(x0, x1, tt)) -> c5(U21'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, x1, 0)) -> c5(U21'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U21(x0, tt, x2)) -> c5(U21'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(x0, 0, x2)) -> c5(U21'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U21(tt, x1, x2)) -> c5(U21'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U21(0, x1, x2)) -> c5(U21'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) 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_U11(z0, z1))) -> c6(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U21(z0, z1, z2))) -> c6(S(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c6(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c6(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_s(cons_and(z0, z1))) -> c6(S(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_s(cons_isNat(z0))) -> c6(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_active(z0))) -> c7(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c7(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c7(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U21(z0, z1, z2))) -> c7(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c7(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c7(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_and(z0, z1))) -> c7(PLUS(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c7(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(cons_active(z0), x1)) -> c7(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c7(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c7(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0, z1, z2), x1)) -> c7(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c7(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c7(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_and(z0, z1), x1)) -> c7(PLUS(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c7(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c7(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c7(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c7(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c7(PLUS(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(x0, cons_active(z0))) -> c8(AND(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_and(x0, cons_mark(z0))) -> c8(AND(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_and(x0, cons_U11(z0, z1))) -> c8(AND(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_and(x0, cons_U21(z0, z1, z2))) -> c8(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_and(x0, cons_s(z0))) -> c8(AND(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_and(x0, cons_plus(z0, z1))) -> c8(AND(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_and(x0, cons_and(z0, z1))) -> c8(AND(encArg(x0), and(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_and(z0, z1))) ENCARG(cons_and(x0, cons_isNat(z0))) -> c8(AND(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_and(cons_active(z0), x1)) -> c8(AND(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_and(cons_mark(z0), x1)) -> c8(AND(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_and(cons_U11(z0, z1), x1)) -> c8(AND(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_U21(z0, z1, z2), x1)) -> c8(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U21(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_and(cons_s(z0), x1)) -> c8(AND(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_and(cons_plus(z0, z1), x1)) -> c8(AND(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_and(z0, z1), x1)) -> c8(AND(and(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_and(z0, z1)), ENCARG(x1)) ENCARG(cons_and(cons_isNat(z0), x1)) -> c8(AND(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_and(x0, tt)) -> c8(AND(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_and(x0, 0)) -> c8(AND(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_and(tt, x1)) -> c8(AND(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_and(0, x1)) -> c8(AND(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_isNat(cons_active(z0))) -> c9(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c9(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c9(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U21(z0, z1, z2))) -> c9(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U21(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c9(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c9(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_and(z0, z1))) -> c9(ISNAT(and(encArg(z0), encArg(z1))), ENCARG(cons_and(z0, z1))) ENCARG(cons_isNat(cons_isNat(z0))) -> c9(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U21(z0, z1, z2)) -> c(ACTIVE(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_s(z0)) -> c(ACTIVE(s(encArg(z0)))) ENCODE_ACTIVE(cons_plus(z0, z1)) -> c(ACTIVE(plus(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_and(z0, z1)) -> c(ACTIVE(and(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_U11(x0, tt) -> c(U11'(encArg(x0), tt)) ENCODE_U11(x0, 0) -> c(U11'(encArg(x0), 0)) ENCODE_U11(x0, cons_active(z0)) -> c(U11'(encArg(x0), active(encArg(z0)))) ENCODE_U11(x0, cons_mark(z0)) -> c(U11'(encArg(x0), mark(encArg(z0)))) ENCODE_U11(x0, cons_U11(z0, z1)) -> c(U11'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U21(z0, z1, z2)) -> c(U11'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_s(z0)) -> c(U11'(encArg(x0), s(encArg(z0)))) ENCODE_U11(x0, cons_plus(z0, z1)) -> c(U11'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_and(z0, z1)) -> c(U11'(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(tt, x1) -> c(U11'(tt, encArg(x1))) ENCODE_U11(0, x1) -> c(U11'(0, encArg(x1))) ENCODE_U11(cons_active(z0), x1) -> c(U11'(active(encArg(z0)), encArg(x1))) ENCODE_U11(cons_mark(z0), x1) -> c(U11'(mark(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U11(z0, z1), x1) -> c(U11'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U21(z0, z1, z2), x1) -> c(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_s(z0), x1) -> c(U11'(s(encArg(z0)), encArg(x1))) ENCODE_U11(cons_plus(z0, z1), x1) -> c(U11'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_and(z0, z1), x1) -> c(U11'(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), 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_U11(z0, z1)) -> c(MARK(U11(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U21(z0, z1, z2)) -> c(MARK(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_s(z0)) -> c(MARK(s(encArg(z0)))) ENCODE_MARK(cons_plus(z0, z1)) -> c(MARK(plus(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_and(z0, z1)) -> c(MARK(and(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_U21(x0, x1, tt) -> c(U21'(encArg(x0), encArg(x1), tt)) ENCODE_U21(x0, x1, 0) -> c(U21'(encArg(x0), encArg(x1), 0)) ENCODE_U21(x0, x1, cons_active(z0)) -> c(U21'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U21(x0, x1, cons_mark(z0)) -> c(U21'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U21(x0, x1, cons_U11(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_U21(z0, z1, z2)) -> c(U21'(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(x0, x1, cons_s(z0)) -> c(U21'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U21(x0, x1, cons_plus(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_and(z0, z1)) -> c(U21'(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))) ENCODE_U21(x0, x1, cons_isNat(z0)) -> c(U21'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U21(x0, tt, x2) -> c(U21'(encArg(x0), tt, encArg(x2))) ENCODE_U21(x0, 0, x2) -> c(U21'(encArg(x0), 0, encArg(x2))) ENCODE_U21(x0, cons_active(z0), x2) -> c(U21'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_mark(z0), x2) -> c(U21'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_U11(z0, z1), x2) -> c(U21'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_U21(z0, z1, z2), x2) -> c(U21'(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U21(x0, cons_s(z0), x2) -> c(U21'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U21(x0, cons_plus(z0, z1), x2) -> c(U21'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_and(z0, z1), x2) -> c(U21'(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U21(x0, cons_isNat(z0), x2) -> c(U21'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U21(tt, x1, x2) -> c(U21'(tt, encArg(x1), encArg(x2))) ENCODE_U21(0, x1, x2) -> c(U21'(0, encArg(x1), encArg(x2))) ENCODE_U21(cons_active(z0), x1, x2) -> c(U21'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_mark(z0), x1, x2) -> c(U21'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U11(z0, z1), x1, x2) -> c(U21'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_U21(z0, z1, z2), x1, x2) -> c(U21'(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U21(cons_s(z0), x1, x2) -> c(U21'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U21(cons_plus(z0, z1), x1, x2) -> c(U21'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_and(z0, z1), x1, x2) -> c(U21'(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U21(cons_isNat(z0), x1, x2) -> c(U21'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_S(cons_active(z0)) -> c(S(active(encArg(z0)))) ENCODE_S(cons_mark(z0)) -> c(S(mark(encArg(z0)))) ENCODE_S(cons_U11(z0, z1)) -> c(S(U11(encArg(z0), encArg(z1)))) ENCODE_S(cons_U21(z0, z1, z2)) -> c(S(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_s(z0)) -> c(S(s(encArg(z0)))) ENCODE_S(cons_plus(z0, z1)) -> c(S(plus(encArg(z0), encArg(z1)))) ENCODE_S(cons_and(z0, z1)) -> c(S(and(encArg(z0), encArg(z1)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) 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_U11(z0, z1)) -> c(PLUS(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U21(z0, z1, z2)) -> c(PLUS(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_s(z0)) -> c(PLUS(encArg(x0), s(encArg(z0)))) ENCODE_PLUS(x0, cons_plus(z0, z1)) -> c(PLUS(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_and(z0, z1)) -> c(PLUS(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U21(z0, z1, z2), x1) -> c(PLUS(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_s(z0), x1) -> c(PLUS(s(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_plus(z0, z1), x1) -> c(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_and(z0, z1), x1) -> c(PLUS(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) 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_U11(z0, z1)) -> c(AND(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_U21(z0, z1, z2)) -> c(AND(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_AND(x0, cons_s(z0)) -> c(AND(encArg(x0), s(encArg(z0)))) ENCODE_AND(x0, cons_plus(z0, z1)) -> c(AND(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_and(z0, z1)) -> c(AND(encArg(x0), and(encArg(z0), encArg(z1)))) ENCODE_AND(x0, cons_isNat(z0)) -> c(AND(encArg(x0), isNat(encArg(z0)))) 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_U11(z0, z1), x1) -> c(AND(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_U21(z0, z1, z2), x1) -> c(AND(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_AND(cons_s(z0), x1) -> c(AND(s(encArg(z0)), encArg(x1))) ENCODE_AND(cons_plus(z0, z1), x1) -> c(AND(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_and(z0, z1), x1) -> c(AND(and(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_AND(cons_isNat(z0), x1) -> c(AND(isNat(encArg(z0)), encArg(x1))) ENCODE_ISNAT(cons_active(z0)) -> c(ISNAT(active(encArg(z0)))) ENCODE_ISNAT(cons_mark(z0)) -> c(ISNAT(mark(encArg(z0)))) ENCODE_ISNAT(cons_U11(z0, z1)) -> c(ISNAT(U11(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U21(z0, z1, z2)) -> c(ISNAT(U21(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_s(z0)) -> c(ISNAT(s(encArg(z0)))) ENCODE_ISNAT(cons_plus(z0, z1)) -> c(ISNAT(plus(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_and(z0, z1)) -> c(ISNAT(and(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_active(cons_active(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) 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_U11(x0, tt))) -> c2(ACTIVE(U11(encArg(x0), tt)), ENCARG(cons_U11(x0, tt))) ENCARG(cons_active(cons_U11(x0, 0))) -> c2(ACTIVE(U11(encArg(x0), 0)), ENCARG(cons_U11(x0, 0))) ENCARG(cons_active(cons_U11(x0, cons_active(z0)))) -> c2(ACTIVE(U11(encArg(x0), active(encArg(z0)))), ENCARG(cons_U11(x0, cons_active(z0)))) ENCARG(cons_active(cons_U11(x0, cons_mark(z0)))) -> c2(ACTIVE(U11(encArg(x0), mark(encArg(z0)))), ENCARG(cons_U11(x0, cons_mark(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U11(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_s(z0)))) -> c2(ACTIVE(U11(encArg(x0), s(encArg(z0)))), ENCARG(cons_U11(x0, cons_s(z0)))) ENCARG(cons_active(cons_U11(x0, cons_plus(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_and(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), and(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_and(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_isNat(z0)))) -> c2(ACTIVE(U11(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_U11(x0, cons_isNat(z0)))) ENCARG(cons_active(cons_U11(tt, x1))) -> c2(ACTIVE(U11(tt, encArg(x1))), ENCARG(cons_U11(tt, x1))) ENCARG(cons_active(cons_U11(0, x1))) -> c2(ACTIVE(U11(0, encArg(x1))), ENCARG(cons_U11(0, x1))) ENCARG(cons_active(cons_U11(cons_active(z0), x1))) -> c2(ACTIVE(U11(active(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_active(z0), x1))) ENCARG(cons_active(cons_U11(cons_mark(z0), x1))) -> c2(ACTIVE(U11(mark(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_mark(z0), x1))) ENCARG(cons_active(cons_U11(cons_U11(z0, z1), x1))) -> c2(ACTIVE(U11(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_s(z0), x1))) -> c2(ACTIVE(U11(s(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_s(z0), x1))) ENCARG(cons_active(cons_U11(cons_plus(z0, z1), x1))) -> c2(ACTIVE(U11(plus(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_plus(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_and(z0, z1), x1))) -> c2(ACTIVE(U11(and(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_and(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_isNat(z0), x1))) -> c2(ACTIVE(U11(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_isNat(z0), x1))) ENCARG(cons_active(cons_U21(x0, x1, tt))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), tt)), ENCARG(cons_U21(x0, x1, tt))) ENCARG(cons_active(cons_U21(x0, x1, 0))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), 0)), ENCARG(cons_U21(x0, x1, 0))) ENCARG(cons_active(cons_U21(x0, x1, cons_active(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), active(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_active(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_mark(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), mark(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_mark(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U11(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_U11(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U21(x0, x1, cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_U21(x0, x1, cons_s(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), s(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_s(z0)))) ENCARG(cons_active(cons_U21(x0, x1, cons_plus(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_plus(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_and(z0, z1)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(cons_U21(x0, x1, cons_and(z0, z1)))) ENCARG(cons_active(cons_U21(x0, x1, cons_isNat(z0)))) -> c2(ACTIVE(U21(encArg(x0), encArg(x1), isNat(encArg(z0)))), ENCARG(cons_U21(x0, x1, cons_isNat(z0)))) ENCARG(cons_active(cons_U21(x0, tt, x2))) -> c2(ACTIVE(U21(encArg(x0), tt, encArg(x2))), ENCARG(cons_U21(x0, tt, x2))) ENCARG(cons_active(cons_U21(x0, 0, x2))) -> c2(ACTIVE(U21(encArg(x0), 0, encArg(x2))), ENCARG(cons_U21(x0, 0, x2))) ENCARG(cons_active(cons_U21(x0, cons_active(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), active(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_active(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_mark(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), mark(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_mark(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_U11(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_U11(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_U21(z0, z1, z2), x2))) -> c2(ACTIVE(U21(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(cons_U21(x0, cons_U21(z0, z1, z2), x2))) ENCARG(cons_active(cons_U21(x0, cons_s(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), s(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_s(z0), x2))) ENCARG(cons_active(cons_U21(x0, cons_plus(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_plus(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_and(z0, z1), x2))) -> c2(ACTIVE(U21(encArg(x0), and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(cons_U21(x0, cons_and(z0, z1), x2))) ENCARG(cons_active(cons_U21(x0, cons_isNat(z0), x2))) -> c2(ACTIVE(U21(encArg(x0), isNat(encArg(z0)), encArg(x2))), ENCARG(cons_U21(x0, cons_isNat(z0), x2))) ENCARG(cons_active(cons_U21(tt, x1, x2))) -> c2(ACTIVE(U21(tt, encArg(x1), encArg(x2))), ENCARG(cons_U21(tt, x1, x2))) ENCARG(cons_active(cons_U21(0, x1, x2))) -> c2(ACTIVE(U21(0, encArg(x1), encArg(x2))), ENCARG(cons_U21(0, x1, x2))) ENCARG(cons_active(cons_U21(cons_active(z0), x1, x2))) -> c2(ACTIVE(U21(active(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_active(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_mark(z0), x1, x2))) -> c2(ACTIVE(U21(mark(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_mark(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_U11(z0, z1), x1, x2))) -> c2(ACTIVE(U21(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U11(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_U21(z0, z1, z2), x1, x2))) -> c2(ACTIVE(U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_U21(z0, z1, z2), x1, x2))) ENCARG(cons_active(cons_U21(cons_s(z0), x1, x2))) -> c2(ACTIVE(U21(s(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_s(z0), x1, x2))) ENCARG(cons_active(cons_U21(cons_plus(z0, z1), x1, x2))) -> c2(ACTIVE(U21(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_plus(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_and(z0, z1), x1, x2))) -> c2(ACTIVE(U21(and(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_and(z0, z1), x1, x2))) ENCARG(cons_active(cons_U21(cons_isNat(z0), x1, x2))) -> c2(ACTIVE(U21(isNat(encArg(z0)), encArg(x1), encArg(x2))), ENCARG(cons_U21(cons_isNat(z0), x1, x2))) 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_U11(z0, z1)))) -> c2(ACTIVE(s(U11(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_active(cons_s(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_s(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c2(ACTIVE(s(plus(encArg(z0), encArg(z1)))), ENCARG(cons_s(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c2(ACTIVE(s(isNat(encArg(z0)))), ENCARG(cons_s(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c2(ACTIVE(plus(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_plus(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_plus(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(plus(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_plus(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(plus(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_plus(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(plus(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_plus(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_plus(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_plus(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(plus(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_plus(cons_isNat(z0), x1))) 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_U11(z0, z1)))) -> c2(ACTIVE(and(encArg(x0), U11(encArg(z0), encArg(z1)))), ENCARG(cons_and(x0, cons_U11(z0, z1)))) ENCARG(cons_active(cons_and(x0, cons_U21(z0, z1, z2)))) -> c2(ACTIVE(and(encArg(x0), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_and(x0, cons_U21(z0, z1, z2)))) 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_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_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_isNat(z0)))) -> c2(ACTIVE(and(encArg(x0), isNat(encArg(z0)))), ENCARG(cons_and(x0, cons_isNat(z0)))) 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_U11(z0, z1), x1))) -> c2(ACTIVE(and(U11(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_and(cons_U11(z0, z1), x1))) ENCARG(cons_active(cons_and(cons_U21(z0, z1, z2), x1))) -> c2(ACTIVE(and(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_and(cons_U21(z0, z1, z2), 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_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_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_isNat(z0), x1))) -> c2(ACTIVE(and(isNat(encArg(z0)), encArg(x1))), ENCARG(cons_and(cons_isNat(z0), x1))) ENCARG(cons_active(cons_isNat(cons_active(z0)))) -> c2(ACTIVE(isNat(active(encArg(z0)))), ENCARG(cons_isNat(cons_active(z0)))) ENCARG(cons_active(cons_isNat(cons_mark(z0)))) -> c2(ACTIVE(isNat(mark(encArg(z0)))), ENCARG(cons_isNat(cons_mark(z0)))) ENCARG(cons_active(cons_isNat(cons_U11(z0, z1)))) -> c2(ACTIVE(isNat(U11(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_U11(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_U21(z0, z1, z2)))) -> c2(ACTIVE(isNat(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_isNat(cons_U21(z0, z1, z2)))) ENCARG(cons_active(cons_isNat(cons_s(z0)))) -> c2(ACTIVE(isNat(s(encArg(z0)))), ENCARG(cons_isNat(cons_s(z0)))) ENCARG(cons_active(cons_isNat(cons_plus(z0, z1)))) -> c2(ACTIVE(isNat(plus(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_plus(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_and(z0, z1)))) -> c2(ACTIVE(isNat(and(encArg(z0), encArg(z1)))), ENCARG(cons_isNat(cons_and(z0, z1)))) ENCARG(cons_active(cons_isNat(cons_isNat(z0)))) -> c2(ACTIVE(isNat(isNat(encArg(z0)))), ENCARG(cons_isNat(cons_isNat(z0)))) ENCARG(cons_active(cons_isNat(0))) -> c2(ACTIVE(isNat(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_U11(z0, z1)))) -> c3(MARK(active(U11(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_active(cons_U21(z0, z1, z2)))) -> c3(MARK(active(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(active(plus(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) 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_U11(z0, z1)))) -> c3(MARK(mark(U11(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U11(z0, z1)))) ENCARG(cons_mark(cons_mark(cons_U21(z0, z1, z2)))) -> c3(MARK(mark(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U21(z0, z1, z2)))) 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_plus(z0, z1)))) -> c3(MARK(mark(plus(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_plus(z0, z1)))) 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_isNat(z0)))) -> c3(MARK(mark(isNat(encArg(z0)))), ENCARG(cons_mark(cons_isNat(z0)))) ENCARG(cons_mark(cons_mark(tt))) -> c10(MARK(mark(tt))) ENCARG(cons_mark(cons_mark(tt))) -> c10(ENCARG(cons_mark(tt))) ENCARG(cons_mark(cons_mark(0))) -> c10(MARK(mark(0))) ENCARG(cons_mark(cons_mark(0))) -> c10(ENCARG(cons_mark(0))) ENCARG(cons_U11(x0, cons_U11(x1, tt))) -> c4(U11'(encArg(x0), U11(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_U11(x1, tt))) ENCARG(cons_U11(x0, cons_U11(x1, 0))) -> c4(U11'(encArg(x0), U11(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_U11(x1, 0))) ENCARG(cons_U11(x0, cons_U11(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U11(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U11(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U11(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U11(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U11(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U11(tt, x2))) -> c4(U11'(encArg(x0), U11(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(tt, x2))) ENCARG(cons_U11(x0, cons_U11(0, x2))) -> c4(U11'(encArg(x0), U11(0, encArg(x2))), ENCARG(x0), ENCARG(cons_U11(0, x2))) ENCARG(cons_U11(x0, cons_U11(cons_active(z0), x2))) -> c4(U11'(encArg(x0), U11(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), U11(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), U11(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_U11(cons_s(z0), x2))) -> c4(U11'(encArg(x0), U11(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_U11(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), U11(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_U11(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), U11(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_U11(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_U11(x1, x2))) -> c4(U11'(active(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_U11(x1, x2))) -> c4(U11'(mark(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U11(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U11(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U11(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_U11(x1, x2))) -> c4(U11'(s(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U11(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_U11(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), U11(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_U11(x1, x2))) -> c4(U11'(isNat(encArg(z0)), U11(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(tt, cons_U11(x1, x2))) -> c4(U11'(tt, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(0, cons_U11(x1, x2))) -> c4(U11'(0, U11(encArg(x1), encArg(x2))), ENCARG(cons_U11(x1, x2))) ENCARG(cons_U11(x0, cons_U21(x1, x2, tt))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), tt)), ENCARG(x0), ENCARG(cons_U21(x1, x2, tt))) ENCARG(cons_U11(x0, cons_U21(x1, x2, 0))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), 0)), ENCARG(x0), ENCARG(cons_U21(x1, x2, 0))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_active(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_active(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_mark(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_s(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_s(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_U21(x1, x2, cons_isNat(z0)))) -> c4(U11'(encArg(x0), U21(encArg(x1), encArg(x2), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_U21(x1, x2, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_U21(x1, tt, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), tt, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, tt, x3))) ENCARG(cons_U11(x0, cons_U21(x1, 0, x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), 0, encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, 0, x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_active(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), active(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_active(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_mark(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), mark(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_mark(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U11(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U11(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U11(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_U21(z0, z1, z2), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_U21(z0, z1, z2), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_s(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), s(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_s(z0), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_plus(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), plus(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_plus(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_and(z0, z1), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), and(encArg(z0), encArg(z1)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_and(z0, z1), x3))) ENCARG(cons_U11(x0, cons_U21(x1, cons_isNat(z0), x3))) -> c4(U11'(encArg(x0), U21(encArg(x1), isNat(encArg(z0)), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(x1, cons_isNat(z0), x3))) ENCARG(cons_U11(x0, cons_U21(tt, x2, x3))) -> c4(U11'(encArg(x0), U21(tt, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(tt, x2, x3))) ENCARG(cons_U11(x0, cons_U21(0, x2, x3))) -> c4(U11'(encArg(x0), U21(0, encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(0, x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_active(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(active(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_active(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_mark(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(mark(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_mark(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U11(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(U11(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U11(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_U21(z0, z1, z2), x2, x3))) -> c4(U11'(encArg(x0), U21(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_U21(z0, z1, z2), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_s(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(s(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_s(z0), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_plus(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(plus(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_plus(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_and(z0, z1), x2, x3))) -> c4(U11'(encArg(x0), U21(and(encArg(z0), encArg(z1)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_and(z0, z1), x2, x3))) ENCARG(cons_U11(x0, cons_U21(cons_isNat(z0), x2, x3))) -> c4(U11'(encArg(x0), U21(isNat(encArg(z0)), encArg(x2), encArg(x3))), ENCARG(x0), ENCARG(cons_U21(cons_isNat(z0), x2, x3))) ENCARG(cons_U11(cons_active(z0), cons_U21(x1, x2, x3))) -> c4(U11'(active(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_active(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_mark(z0), cons_U21(x1, x2, x3))) -> c4(U11'(mark(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_mark(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U11(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(U11(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_U21(x1, x2, x3))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_s(z0), cons_U21(x1, x2, x3))) -> c4(U11'(s(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_s(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_plus(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(plus(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_and(z0, z1), cons_U21(x1, x2, x3))) -> c4(U11'(and(encArg(z0), encArg(z1)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_and(z0, z1)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(cons_isNat(z0), cons_U21(x1, x2, x3))) -> c4(U11'(isNat(encArg(z0)), U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_isNat(z0)), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(tt, cons_U21(x1, x2, x3))) -> c4(U11'(tt, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(0, cons_U21(x1, x2, x3))) -> c4(U11'(0, U21(encArg(x1), encArg(x2), encArg(x3))), ENCARG(cons_U21(x1, x2, x3))) ENCARG(cons_U11(x0, cons_s(cons_active(z0)))) -> c4(U11'(encArg(x0), s(active(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_active(z0)))) ENCARG(cons_U11(x0, cons_s(cons_mark(z0)))) -> c4(U11'(encArg(x0), s(mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_mark(z0)))) ENCARG(cons_U11(x0, cons_s(cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), s(U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), s(U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_s(cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_s(cons_s(z0)))) -> c4(U11'(encArg(x0), s(s(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_s(z0)))) ENCARG(cons_U11(x0, cons_s(cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), s(plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_and(z0, z1)))) -> c4(U11'(encArg(x0), s(and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_s(cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_s(cons_isNat(z0)))) -> c4(U11'(encArg(x0), s(isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_s(cons_isNat(z0)))) ENCARG(cons_U11(cons_active(z0), cons_s(x1))) -> c4(U11'(active(encArg(z0)), s(encArg(x1))), ENCARG(cons_active(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_mark(z0), cons_s(x1))) -> c4(U11'(mark(encArg(z0)), s(encArg(x1))), ENCARG(cons_mark(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U11(z0, z1), cons_s(x1))) -> c4(U11'(U11(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_s(x1))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), s(encArg(x1))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_s(z0), cons_s(x1))) -> c4(U11'(s(encArg(z0)), s(encArg(x1))), ENCARG(cons_s(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_plus(z0, z1), cons_s(x1))) -> c4(U11'(plus(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_and(z0, z1), cons_s(x1))) -> c4(U11'(and(encArg(z0), encArg(z1)), s(encArg(x1))), ENCARG(cons_and(z0, z1)), ENCARG(cons_s(x1))) ENCARG(cons_U11(cons_isNat(z0), cons_s(x1))) -> c4(U11'(isNat(encArg(z0)), s(encArg(x1))), ENCARG(cons_isNat(z0)), ENCARG(cons_s(x1))) ENCARG(cons_U11(x0, cons_s(tt))) -> c4(U11'(encArg(x0), s(tt)), ENCARG(x0)) ENCARG(cons_U11(x0, cons_s(0))) -> c4(U11'(encArg(x0), s(0)), ENCARG(x0)) ENCARG(cons_U11(tt, cons_s(x1))) -> c4(U11'(tt, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_U11(0, cons_s(x1))) -> c4(U11'(0, s(encArg(x1))), ENCARG(cons_s(x1))) ENCARG(cons_U11(x0, cons_plus(x1, tt))) -> c4(U11'(encArg(x0), plus(encArg(x1), tt)), ENCARG(x0), ENCARG(cons_plus(x1, tt))) ENCARG(cons_U11(x0, cons_plus(x1, 0))) -> c4(U11'(encArg(x0), plus(encArg(x1), 0)), ENCARG(x0), ENCARG(cons_plus(x1, 0))) ENCARG(cons_U11(x0, cons_plus(x1, cons_active(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), active(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_active(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_mark(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), mark(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_mark(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_U11(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), U11(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_U11(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_U21(z0, z1, z2)))) -> c4(U11'(encArg(x0), plus(encArg(x1), U21(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_U21(z0, z1, z2)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_s(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), s(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_s(z0)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_plus(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), plus(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_plus(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_and(z0, z1)))) -> c4(U11'(encArg(x0), plus(encArg(x1), and(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_and(z0, z1)))) ENCARG(cons_U11(x0, cons_plus(x1, cons_isNat(z0)))) -> c4(U11'(encArg(x0), plus(encArg(x1), isNat(encArg(z0)))), ENCARG(x0), ENCARG(cons_plus(x1, cons_isNat(z0)))) ENCARG(cons_U11(x0, cons_plus(tt, x2))) -> c4(U11'(encArg(x0), plus(tt, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(tt, x2))) ENCARG(cons_U11(x0, cons_plus(0, x2))) -> c4(U11'(encArg(x0), plus(0, encArg(x2))), ENCARG(x0), ENCARG(cons_plus(0, x2))) ENCARG(cons_U11(x0, cons_plus(cons_active(z0), x2))) -> c4(U11'(encArg(x0), plus(active(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_active(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_mark(z0), x2))) -> c4(U11'(encArg(x0), plus(mark(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_mark(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_U11(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(U11(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_U11(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_U21(z0, z1, z2), x2))) -> c4(U11'(encArg(x0), plus(U21(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_U21(z0, z1, z2), x2))) ENCARG(cons_U11(x0, cons_plus(cons_s(z0), x2))) -> c4(U11'(encArg(x0), plus(s(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_s(z0), x2))) ENCARG(cons_U11(x0, cons_plus(cons_plus(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(plus(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_plus(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_and(z0, z1), x2))) -> c4(U11'(encArg(x0), plus(and(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_and(z0, z1), x2))) ENCARG(cons_U11(x0, cons_plus(cons_isNat(z0), x2))) -> c4(U11'(encArg(x0), plus(isNat(encArg(z0)), encArg(x2))), ENCARG(x0), ENCARG(cons_plus(cons_isNat(z0), x2))) ENCARG(cons_U11(cons_active(z0), cons_plus(x1, x2))) -> c4(U11'(active(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_active(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_mark(z0), cons_plus(x1, x2))) -> c4(U11'(mark(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_mark(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_U11(z0, z1), cons_plus(x1, x2))) -> c4(U11'(U11(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_U11(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_U21(z0, z1, z2), cons_plus(x1, x2))) -> c4(U11'(U21(encArg(z0), encArg(z1), encArg(z2)), plus(encArg(x1), encArg(x2))), ENCARG(cons_U21(z0, z1, z2)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_s(z0), cons_plus(x1, x2))) -> c4(U11'(s(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_s(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_plus(z0, z1), cons_plus(x1, x2))) -> c4(U11'(plus(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_and(z0, z1), cons_plus(x1, x2))) -> c4(U11'(and(encArg(z0), encArg(z1)), plus(encArg(x1), encArg(x2))), ENCARG(cons_and(z0, z1)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(cons_isNat(z0), cons_plus(x1, x2))) -> c4(U11'(isNat(encArg(z0)), plus(encArg(x1), encArg(x2))), ENCARG(cons_isNat(z0)), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(tt, cons_plus(x1, x2))) -> c4(U11'(tt, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) ENCARG(cons_U11(0, cons_plus(x1, x2))) -> c4(U11'(0, plus(encArg(x1), encArg(x2))), ENCARG(cons_plus(x1, x2))) S tuples: ACTIVE(U11(tt, z0)) -> c20(MARK(z0)) ACTIVE(and(tt, z0)) -> c22(MARK(z0)) ACTIVE(isNat(0)) -> c23(MARK(tt)) ACTIVE(isNat(s(z0))) -> c25(MARK(isNat(z0)), ISNAT(z0)) MARK(isNat(z0)) -> c34(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c36(U11'(z0, z1)) U11'(z0, mark(z1)) -> c37(U11'(z0, z1)) U11'(active(z0), z1) -> c38(U11'(z0, z1)) U11'(z0, active(z1)) -> c39(U11'(z0, z1)) U21'(mark(z0), z1, z2) -> c40(U21'(z0, z1, z2)) U21'(z0, mark(z1), z2) -> c41(U21'(z0, z1, z2)) U21'(z0, z1, mark(z2)) -> c42(U21'(z0, z1, z2)) U21'(active(z0), z1, z2) -> c43(U21'(z0, z1, z2)) U21'(z0, active(z1), z2) -> c44(U21'(z0, z1, z2)) U21'(z0, z1, active(z2)) -> c45(U21'(z0, z1, z2)) S(mark(z0)) -> c46(S(z0)) S(active(z0)) -> c47(S(z0)) PLUS(mark(z0), z1) -> c48(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c49(PLUS(z0, z1)) PLUS(active(z0), z1) -> c50(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c51(PLUS(z0, z1)) AND(mark(z0), z1) -> c52(AND(z0, z1)) AND(z0, mark(z1)) -> c53(AND(z0, z1)) AND(active(z0), z1) -> c54(AND(z0, z1)) AND(z0, active(z1)) -> c55(AND(z0, z1)) ISNAT(mark(z0)) -> c56(ISNAT(z0)) ISNAT(active(z0)) -> c57(ISNAT(z0)) ACTIVE(U21(tt, z0, z1)) -> c21(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(plus(z0, z1))) -> c24(MARK(and(isNat(z0), isNat(z1))), ISNAT(z0), ISNAT(z1)) ACTIVE(plus(z0, 0)) -> c26(MARK(U11(isNat(z0), z0)), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c27(MARK(U21(and(isNat(z1), isNat(z0)), z1, z0)), ISNAT(z1), ISNAT(z0)) MARK(tt) -> c29 MARK(0) -> c35 MARK(U11(z0, z1)) -> c28(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c28(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c28(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U21(z0, z1, z2), x1)) -> c28(ACTIVE(U11(active(U21(mark(z0), z1, z2)), x1)), U11'(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c28(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c28(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c28(ACTIVE(U11(active(and(mark(z0), z1)), x1)), U11'(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c28(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(0, x1)) -> c28(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c28(U11'(mark(x0), x1)) MARK(U21(z0, z1, z2)) -> c30(ACTIVE(U21(z0, z1, z2)), U21'(mark(z0), z1, z2), MARK(z0)) MARK(U21(U11(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(U11(mark(z0), z1)), x1, x2)), U21'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U21(tt, x1, x2)) -> c30(ACTIVE(U21(active(tt), x1, x2)), U21'(mark(tt), x1, x2), MARK(tt)) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c30(ACTIVE(U21(active(U21(mark(z0), z1, z2)), x1, x2)), U21'(mark(U21(z0, z1, z2)), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(s(z0), x1, x2)) -> c30(ACTIVE(U21(active(s(mark(z0))), x1, x2)), U21'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U21(plus(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(plus(mark(z0), mark(z1))), x1, x2)), U21'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c30(ACTIVE(U21(active(and(mark(z0), z1)), x1, x2)), U21'(mark(and(z0, z1)), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c30(ACTIVE(U21(active(isNat(z0)), x1, x2)), U21'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U21(0, x1, x2)) -> c30(ACTIVE(U21(active(0), x1, x2)), U21'(mark(0), x1, x2), MARK(0)) MARK(U21(x0, x1, x2)) -> c30(U21'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c31(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c31(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U21(z0, z1, z2))) -> c31(ACTIVE(s(active(U21(mark(z0), z1, z2)))), S(mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2))) MARK(s(s(z0))) -> c31(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c31(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(and(z0, z1))) -> c31(ACTIVE(s(active(and(mark(z0), z1)))), S(mark(and(z0, z1))), MARK(and(z0, z1))) MARK(s(isNat(z0))) -> c31(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(0)) -> c31(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c31(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c32(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c32(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c32(ACTIVE(plus(mark(x0), active(U11(mark(z0), z1)))), PLUS(mark(x0), mark(U11(z0, z1))), MARK(x0), MARK(U11(z0, z1))) MARK(plus(x0, tt)) -> c32(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U21(z0, z1, z2))) -> c32(ACTIVE(plus(mark(x0), active(U21(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U21(z0, z1, z2))), MARK(x0), MARK(U21(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c32(ACTIVE(plus(mark(x0), active(s(mark(z0))))), PLUS(mark(x0), mark(s(z0))), MARK(x0), MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c32(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, and(z0, z1))) -> c32(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, isNat(z0))) -> c32(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, 0)) -> c32(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c32(ACTIVE(plus(active(U11(mark(z0), z1)), mark(x1))), PLUS(mark(U11(z0, z1)), mark(x1)), MARK(U11(z0, z1)), MARK(x1)) MARK(plus(tt, x1)) -> c32(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c32(ACTIVE(plus(active(U21(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U21(z0, z1, z2)), mark(x1)), MARK(U21(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c32(ACTIVE(plus(active(s(mark(z0))), mark(x1))), PLUS(mark(s(z0)), mark(x1)), MARK(s(z0)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c32(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(and(z0, z1), x1)) -> c32(ACTIVE(plus(active(and(mark(z0), z1)), mark(x1))), PLUS(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c32(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(0, x1)) -> c32(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) MARK(and(z0, z1)) -> c33(ACTIVE(and(z0, z1)), AND(mark(z0), z1), MARK(z0)) MARK(and(U11(z0, z1), x1)) -> c33(ACTIVE(and(active(U11(mark(z0), z1)), x1)), AND(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(and(tt, x1)) -> c33(ACTIVE(and(active(tt), x1)), AND(mark(tt), x1), MARK(tt)) MARK(and(U21(z0, z1, z2), x1)) -> c33(ACTIVE(and(active(U21(mark(z0), z1, z2)), x1)), AND(mark(U21(z0, z1, z2)), x1), MARK(U21(z0, z1, z2))) MARK(and(s(z0), x1)) -> c33(ACTIVE(and(active(s(mark(z0))), x1)), AND(mark(s(z0)), x1), MARK(s(z0))) MARK(and(plus(z0, z1), x1)) -> c33(ACTIVE(and(active(plus(mark(z0), mark(z1))), x1)), AND(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c33(ACTIVE(and(active(and(mark(z0), z1)), x1)), AND(mark(and(z0, z1)), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c33(ACTIVE(and(active(isNat(z0)), x1)), AND(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(and(0, x1)) -> c33(ACTIVE(and(active(0), x1)), AND(mark(0), x1), MARK(0)) MARK(and(x0, x1)) -> c33(AND(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U21_3, s_1, plus_2, and_2, isNat_1 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U21'_3, S_1, PLUS_2, AND_2, ISNAT_1, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U21_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_AND_2, ENCODE_ISNAT_1 Compound Symbols: c20_1, c22_1, c23_1, c25_2, c34_2, c36_1, c37_1, c38_1, c39_1, c40_1, c41_1, c42_1, c43_1, c44_1, c45_1, c46_1, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c21_2, c24_3, c26_2, c27_3, c29, c35, c3_2, c3_1, c4_3, c4_2, c5_4, c5_3, c6_2, c7_3, c7_2, c8_3, c8_2, c9_2, c28_3, c28_1, c30_3, c30_1, c31_3, c31_2, c32_4, c33_3, c33_1, c_1, c2_2, c1_1, c2_1, c10_1