/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 546 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 11 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 80.1 s] (14) BOUNDS(1, INF) (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 3 ms] (24) CpxTypedWeightedCompleteTrs (25) CompletionProof [UPPER BOUND(ID), 6 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (30) CdtProblem (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (38) CdtProblem (39) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 73 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (42) CdtProblem (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 187 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 217 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 168 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 92 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 29 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms] (110) CdtProblem (111) CdtLeafRemovalProof [ComplexityIfPolyImplication, 24 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 21 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms] (142) CdtProblem (143) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 104 ms] (146) 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, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0)) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_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, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0)) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_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, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0)) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0)) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0')) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0')) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0' Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: active(U11(tt, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0')) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0')) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0' Types: active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U31 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U41 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U42 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus 0' :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encArg :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U31 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U41 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U42 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U31 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U41 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U42 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_0 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus hole_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus1_4 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4 :: Nat -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: active, mark, U12, isNat, U42, s, plus, U11, U21, U31, U41, encArg They will be analysed ascendingly in the following order: active = mark U12 < active isNat < active U42 < active s < active plus < active U11 < active U21 < active U31 < active U41 < active active < encArg U12 < mark isNat < mark U42 < mark s < mark plus < mark U11 < mark U21 < mark U31 < mark U41 < mark mark < encArg U12 < encArg isNat < encArg U42 < encArg s < encArg plus < encArg U11 < encArg U21 < encArg U31 < encArg U41 < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: active(U11(tt, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0')) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0')) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0' Types: active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U31 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U41 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U42 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus 0' :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encArg :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U31 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U41 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U42 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_active :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U11 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_tt :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_mark :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U12 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_isNat :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U21 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U31 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U41 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U42 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_s :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_plus :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_0 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus hole_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus1_4 :: tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4 :: Nat -> tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus Generator Equations: gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4(0) <=> tt gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4(+(x, 1)) <=> cons_active(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4(x)) The following defined symbols remain to be analysed: U12, active, mark, isNat, U42, s, plus, U11, U21, U31, U41, encArg They will be analysed ascendingly in the following order: active = mark U12 < active isNat < active U42 < active s < active plus < active U11 < active U21 < active U31 < active U41 < active active < encArg U12 < mark isNat < mark U42 < mark s < mark plus < mark U11 < mark U21 < mark U31 < mark U41 < mark mark < encArg U12 < encArg isNat < encArg U42 < encArg s < encArg plus < encArg U11 < encArg U21 < encArg U31 < encArg U41 < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4(+(1, n37508_4))) -> *3_4, rt in Omega(0) Induction Base: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4(+(1, 0))) Induction Step: encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4(+(1, +(n37508_4, 1)))) ->_R^Omega(0) active(encArg(gen_tt:0':cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus2_4(+(1, n37508_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). ---------------------------------------- (14) BOUNDS(1, INF) ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: active(U11(tt, V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, N)) -> mark(N) active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) active(U42(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N, 0)) -> mark(U31(isNat(N), N)) active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) mark(U11(X1, X2)) -> active(U11(mark(X1), X2)) mark(tt) -> active(tt) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1, X2)) -> active(U31(mark(X1), X2)) mark(U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) mark(U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1, X2)) -> active(plus(mark(X1), mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1), X2) -> U31(X1, X2) U31(X1, mark(X2)) -> U31(X1, X2) U31(active(X1), X2) -> U31(X1, X2) U31(X1, active(X2)) -> U31(X1, X2) U41(mark(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, mark(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, mark(X3)) -> U41(X1, X2, X3) U41(active(X1), X2, X3) -> U41(X1, X2, X3) U41(X1, active(X2), X3) -> U41(X1, X2, X3) U41(X1, X2, active(X3)) -> U41(X1, X2, X3) U42(mark(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, mark(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, mark(X3)) -> U42(X1, X2, X3) U42(active(X1), X2, X3) -> U42(X1, X2, X3) U42(X1, active(X2), X3) -> U42(X1, X2, X3) U42(X1, X2, active(X3)) -> U42(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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_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) U31(X1, c_active(X2)) -> U31(X1, X2) mark(c_U31(X1, X2)) -> active(U31(mark(X1), X2)) isNat(c_active(X)) -> isNat(X) active(c_plus(N, c_s(M))) -> mark(U41(isNat(M), M, N)) mark(c_U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) U41(c_active(X1), X2, X3) -> U41(X1, X2, X3) active(c_plus(N, 0)) -> mark(U31(isNat(N), N)) mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) U42(X1, X2, c_active(X3)) -> U42(X1, X2, X3) U11(X1, c_mark(X2)) -> U11(X1, X2) U31(c_active(X1), X2) -> U31(X1, X2) U41(X1, X2, c_mark(X3)) -> U41(X1, X2, X3) active(c_U21(tt)) -> mark(tt) active(c_isNat(c_s(V1))) -> mark(U21(isNat(V1))) U42(X1, c_mark(X2), X3) -> U42(X1, X2, X3) U31(X1, c_mark(X2)) -> U31(X1, X2) U41(c_mark(X1), X2, X3) -> U41(X1, X2, X3) U42(c_active(X1), X2, X3) -> U42(X1, X2, X3) U12(c_mark(X)) -> U12(X) U12(c_active(X)) -> U12(X) U41(X1, c_active(X2), X3) -> U41(X1, X2, X3) active(c_U12(tt)) -> mark(tt) mark(c_U21(X)) -> active(U21(mark(X))) U42(X1, c_active(X2), X3) -> U42(X1, X2, X3) U41(X1, c_mark(X2), X3) -> U41(X1, X2, X3) U31(c_mark(X1), X2) -> U31(X1, X2) U42(c_mark(X1), X2, X3) -> U42(X1, X2, X3) isNat(c_mark(X)) -> isNat(X) U21(c_active(X)) -> U21(X) active(c_isNat(0)) -> mark(tt) U21(c_mark(X)) -> U21(X) plus(X1, c_mark(X2)) -> plus(X1, X2) mark(c_U12(X)) -> active(U12(mark(X))) active(c_U11(tt, V2)) -> mark(U12(isNat(V2))) active(c_U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) U42(X1, X2, c_mark(X3)) -> U42(X1, X2, X3) plus(c_active(X1), X2) -> plus(X1, X2) mark(c_s(X)) -> active(s(mark(X))) U41(X1, X2, c_active(X3)) -> U41(X1, X2, X3) active(c_isNat(c_plus(V1, V2))) -> mark(U11(isNat(V1), V2)) s(c_active(X)) -> s(X) active(c_U42(tt, M, N)) -> mark(s(plus(N, M))) s(c_mark(X)) -> s(X) mark(c_U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) plus(c_mark(X1), X2) -> plus(X1, X2) U11(c_mark(X1), X2) -> U11(X1, X2) U11(X1, c_active(X2)) -> U11(X1, X2) active(c_U31(tt, N)) -> mark(N) mark(c_isNat(X)) -> active(isNat(X)) 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) 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_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_U42(x_1, x_2, x_3)) -> U42(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)) 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_U12(x_1) -> U12(encArg(x_1)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_U21(x_1) -> U21(encArg(x_1)) encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0 s(x0) -> c_s(x0) U42(x0, x1, x2) -> c_U42(x0, x1, x2) isNat(x0) -> c_isNat(x0) active(x0) -> c_active(x0) U41(x0, x1, x2) -> c_U41(x0, x1, x2) plus(x0, x1) -> c_plus(x0, x1) U12(x0) -> c_U12(x0) U31(x0, x1) -> c_U31(x0, x1) U21(x0) -> c_U21(x0) 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] U31(X1, c_active(X2)) -> U31(X1, X2) [1] mark(c_U31(X1, X2)) -> active(U31(mark(X1), X2)) [1] isNat(c_active(X)) -> isNat(X) [1] active(c_plus(N, c_s(M))) -> mark(U41(isNat(M), M, N)) [1] mark(c_U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) [1] U41(c_active(X1), X2, X3) -> U41(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(U31(isNat(N), N)) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] U42(X1, X2, c_active(X3)) -> U42(X1, X2, X3) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U31(c_active(X1), X2) -> U31(X1, X2) [1] U41(X1, X2, c_mark(X3)) -> U41(X1, X2, X3) [1] active(c_U21(tt)) -> mark(tt) [1] active(c_isNat(c_s(V1))) -> mark(U21(isNat(V1))) [1] U42(X1, c_mark(X2), X3) -> U42(X1, X2, X3) [1] U31(X1, c_mark(X2)) -> U31(X1, X2) [1] U41(c_mark(X1), X2, X3) -> U41(X1, X2, X3) [1] U42(c_active(X1), X2, X3) -> U42(X1, X2, X3) [1] U12(c_mark(X)) -> U12(X) [1] U12(c_active(X)) -> U12(X) [1] U41(X1, c_active(X2), X3) -> U41(X1, X2, X3) [1] active(c_U12(tt)) -> mark(tt) [1] mark(c_U21(X)) -> active(U21(mark(X))) [1] U42(X1, c_active(X2), X3) -> U42(X1, X2, X3) [1] U41(X1, c_mark(X2), X3) -> U41(X1, X2, X3) [1] U31(c_mark(X1), X2) -> U31(X1, X2) [1] U42(c_mark(X1), X2, X3) -> U42(X1, X2, X3) [1] isNat(c_mark(X)) -> isNat(X) [1] U21(c_active(X)) -> U21(X) [1] active(c_isNat(0)) -> mark(tt) [1] U21(c_mark(X)) -> U21(X) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] mark(c_U12(X)) -> active(U12(mark(X))) [1] active(c_U11(tt, V2)) -> mark(U12(isNat(V2))) [1] active(c_U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) [1] U42(X1, X2, c_mark(X3)) -> U42(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U41(X1, X2, c_active(X3)) -> U41(X1, X2, X3) [1] active(c_isNat(c_plus(V1, V2))) -> mark(U11(isNat(V1), V2)) [1] s(c_active(X)) -> s(X) [1] active(c_U42(tt, M, N)) -> mark(s(plus(N, M))) [1] s(c_mark(X)) -> s(X) [1] mark(c_U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) [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] active(c_U31(tt, N)) -> mark(N) [1] mark(c_isNat(X)) -> active(isNat(X)) [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] 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_U12(x_1)) -> U12(encArg(x_1)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encArg(cons_U21(x_1)) -> U21(encArg(x_1)) [0] encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) [0] encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U42(x_1, x_2, x_3)) -> U42(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] 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_U12(x_1) -> U12(encArg(x_1)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_U21(x_1) -> U21(encArg(x_1)) [0] encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) [0] encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0 [0] s(x0) -> c_s(x0) [0] U42(x0, x1, x2) -> c_U42(x0, x1, x2) [0] isNat(x0) -> c_isNat(x0) [0] active(x0) -> c_active(x0) [0] U41(x0, x1, x2) -> c_U41(x0, x1, x2) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0) -> c_U12(x0) [0] U31(x0, x1) -> c_U31(x0, x1) [0] U21(x0) -> c_U21(x0) [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] U31(X1, c_active(X2)) -> U31(X1, X2) [1] mark(c_U31(X1, X2)) -> active(U31(mark(X1), X2)) [1] isNat(c_active(X)) -> isNat(X) [1] active(c_plus(N, c_s(M))) -> mark(U41(isNat(M), M, N)) [1] mark(c_U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) [1] U41(c_active(X1), X2, X3) -> U41(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(U31(isNat(N), N)) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] U42(X1, X2, c_active(X3)) -> U42(X1, X2, X3) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U31(c_active(X1), X2) -> U31(X1, X2) [1] U41(X1, X2, c_mark(X3)) -> U41(X1, X2, X3) [1] active(c_U21(tt)) -> mark(tt) [1] active(c_isNat(c_s(V1))) -> mark(U21(isNat(V1))) [1] U42(X1, c_mark(X2), X3) -> U42(X1, X2, X3) [1] U31(X1, c_mark(X2)) -> U31(X1, X2) [1] U41(c_mark(X1), X2, X3) -> U41(X1, X2, X3) [1] U42(c_active(X1), X2, X3) -> U42(X1, X2, X3) [1] U12(c_mark(X)) -> U12(X) [1] U12(c_active(X)) -> U12(X) [1] U41(X1, c_active(X2), X3) -> U41(X1, X2, X3) [1] active(c_U12(tt)) -> mark(tt) [1] mark(c_U21(X)) -> active(U21(mark(X))) [1] U42(X1, c_active(X2), X3) -> U42(X1, X2, X3) [1] U41(X1, c_mark(X2), X3) -> U41(X1, X2, X3) [1] U31(c_mark(X1), X2) -> U31(X1, X2) [1] U42(c_mark(X1), X2, X3) -> U42(X1, X2, X3) [1] isNat(c_mark(X)) -> isNat(X) [1] U21(c_active(X)) -> U21(X) [1] active(c_isNat(0)) -> mark(tt) [1] U21(c_mark(X)) -> U21(X) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] mark(c_U12(X)) -> active(U12(mark(X))) [1] active(c_U11(tt, V2)) -> mark(U12(isNat(V2))) [1] active(c_U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) [1] U42(X1, X2, c_mark(X3)) -> U42(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U41(X1, X2, c_active(X3)) -> U41(X1, X2, X3) [1] active(c_isNat(c_plus(V1, V2))) -> mark(U11(isNat(V1), V2)) [1] s(c_active(X)) -> s(X) [1] active(c_U42(tt, M, N)) -> mark(s(plus(N, M))) [1] s(c_mark(X)) -> s(X) [1] mark(c_U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) [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] active(c_U31(tt, N)) -> mark(N) [1] mark(c_isNat(X)) -> active(isNat(X)) [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] 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_U12(x_1)) -> U12(encArg(x_1)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encArg(cons_U21(x_1)) -> U21(encArg(x_1)) [0] encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) [0] encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U42(x_1, x_2, x_3)) -> U42(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] 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_U12(x_1) -> U12(encArg(x_1)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_U21(x_1) -> U21(encArg(x_1)) [0] encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) [0] encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0 [0] s(x0) -> c_s(x0) [0] U42(x0, x1, x2) -> c_U42(x0, x1, x2) [0] isNat(x0) -> c_isNat(x0) [0] active(x0) -> c_active(x0) [0] U41(x0, x1, x2) -> c_U41(x0, x1, x2) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0) -> c_U12(x0) [0] U31(x0, x1) -> c_U31(x0, x1) [0] U21(x0) -> c_U21(x0) [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_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus tt :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus 0 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus isNat :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_s :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U41 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_U42 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U42 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_U11 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U11 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_mark :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_U21 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_isNat :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U21 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus U12 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_U12 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus c_U41 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus s :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encArg :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_mark :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U11 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U12 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_isNat :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U21 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U41 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_U42 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_s :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus cons_plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U11 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_tt :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_mark :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U12 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_isNat :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U21 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U41 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_U42 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_s :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus encode_0 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus 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_U12_1 encode_isNat_1 encode_U21_1 encode_U31_2 encode_U41_3 encode_U42_3 encode_s_1 encode_plus_2 encode_0 s_1 U42_3 isNat_1 active_1 U41_3 plus_2 U12_1 U31_2 U21_1 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_U12(v0) -> null_encode_U12 [0] encode_isNat(v0) -> null_encode_isNat [0] encode_U21(v0) -> null_encode_U21 [0] encode_U31(v0, v1) -> null_encode_U31 [0] encode_U41(v0, v1, v2) -> null_encode_U41 [0] encode_U42(v0, v1, v2) -> null_encode_U42 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] s(v0) -> null_s [0] U42(v0, v1, v2) -> null_U42 [0] isNat(v0) -> null_isNat [0] active(v0) -> null_active [0] U41(v0, v1, v2) -> null_U41 [0] plus(v0, v1) -> null_plus [0] U12(v0) -> null_U12 [0] U31(v0, v1) -> null_U31 [0] U21(v0) -> null_U21 [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_U12, null_encode_isNat, null_encode_U21, null_encode_U31, null_encode_U41, null_encode_U42, null_encode_s, null_encode_plus, null_encode_0, null_s, null_U42, null_isNat, null_active, null_U41, null_plus, null_U12, null_U31, null_U21, 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] U31(X1, c_active(X2)) -> U31(X1, X2) [1] mark(c_U31(X1, X2)) -> active(U31(mark(X1), X2)) [1] isNat(c_active(X)) -> isNat(X) [1] active(c_plus(N, c_s(M))) -> mark(U41(isNat(M), M, N)) [1] mark(c_U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) [1] U41(c_active(X1), X2, X3) -> U41(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(U31(isNat(N), N)) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] U42(X1, X2, c_active(X3)) -> U42(X1, X2, X3) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U31(c_active(X1), X2) -> U31(X1, X2) [1] U41(X1, X2, c_mark(X3)) -> U41(X1, X2, X3) [1] active(c_U21(tt)) -> mark(tt) [1] active(c_isNat(c_s(V1))) -> mark(U21(isNat(V1))) [1] U42(X1, c_mark(X2), X3) -> U42(X1, X2, X3) [1] U31(X1, c_mark(X2)) -> U31(X1, X2) [1] U41(c_mark(X1), X2, X3) -> U41(X1, X2, X3) [1] U42(c_active(X1), X2, X3) -> U42(X1, X2, X3) [1] U12(c_mark(X)) -> U12(X) [1] U12(c_active(X)) -> U12(X) [1] U41(X1, c_active(X2), X3) -> U41(X1, X2, X3) [1] active(c_U12(tt)) -> mark(tt) [1] mark(c_U21(X)) -> active(U21(mark(X))) [1] U42(X1, c_active(X2), X3) -> U42(X1, X2, X3) [1] U41(X1, c_mark(X2), X3) -> U41(X1, X2, X3) [1] U31(c_mark(X1), X2) -> U31(X1, X2) [1] U42(c_mark(X1), X2, X3) -> U42(X1, X2, X3) [1] isNat(c_mark(X)) -> isNat(X) [1] U21(c_active(X)) -> U21(X) [1] active(c_isNat(0)) -> mark(tt) [1] U21(c_mark(X)) -> U21(X) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] mark(c_U12(X)) -> active(U12(mark(X))) [1] active(c_U11(tt, V2)) -> mark(U12(isNat(V2))) [1] active(c_U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) [1] U42(X1, X2, c_mark(X3)) -> U42(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U41(X1, X2, c_active(X3)) -> U41(X1, X2, X3) [1] active(c_isNat(c_plus(V1, V2))) -> mark(U11(isNat(V1), V2)) [1] s(c_active(X)) -> s(X) [1] active(c_U42(tt, M, N)) -> mark(s(plus(N, M))) [1] s(c_mark(X)) -> s(X) [1] mark(c_U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) [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] active(c_U31(tt, N)) -> mark(N) [1] mark(c_isNat(X)) -> active(isNat(X)) [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] 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_U12(x_1)) -> U12(encArg(x_1)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encArg(cons_U21(x_1)) -> U21(encArg(x_1)) [0] encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) [0] encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U42(x_1, x_2, x_3)) -> U42(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] 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_U12(x_1) -> U12(encArg(x_1)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_U21(x_1) -> U21(encArg(x_1)) [0] encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) [0] encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0 [0] s(x0) -> c_s(x0) [0] U42(x0, x1, x2) -> c_U42(x0, x1, x2) [0] isNat(x0) -> c_isNat(x0) [0] active(x0) -> c_active(x0) [0] U41(x0, x1, x2) -> c_U41(x0, x1, x2) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0) -> c_U12(x0) [0] U31(x0, x1) -> c_U31(x0, x1) [0] U21(x0) -> c_U21(x0) [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_U12(v0) -> null_encode_U12 [0] encode_isNat(v0) -> null_encode_isNat [0] encode_U21(v0) -> null_encode_U21 [0] encode_U31(v0, v1) -> null_encode_U31 [0] encode_U41(v0, v1, v2) -> null_encode_U41 [0] encode_U42(v0, v1, v2) -> null_encode_U42 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] s(v0) -> null_s [0] U42(v0, v1, v2) -> null_U42 [0] isNat(v0) -> null_isNat [0] active(v0) -> null_active [0] U41(v0, v1, v2) -> null_U41 [0] plus(v0, v1) -> null_plus [0] U12(v0) -> null_U12 [0] U31(v0, v1) -> null_U31 [0] U21(v0) -> null_U21 [0] U11(v0, v1) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark tt :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark 0 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark c_active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark c_U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark isNat :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark c_plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark c_s :: 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tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U12 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U21 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U11 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_mark :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (25) 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_U12(v0) -> null_encode_U12 [0] encode_isNat(v0) -> null_encode_isNat [0] encode_U21(v0) -> null_encode_U21 [0] encode_U31(v0, v1) -> null_encode_U31 [0] encode_U41(v0, v1, v2) -> null_encode_U41 [0] encode_U42(v0, v1, v2) -> null_encode_U42 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] s(v0) -> null_s [0] U42(v0, v1, v2) -> null_U42 [0] isNat(v0) -> null_isNat [0] active(v0) -> null_active [0] U41(v0, v1, v2) -> null_U41 [0] plus(v0, v1) -> null_plus [0] U12(v0) -> null_U12 [0] U31(v0, v1) -> null_U31 [0] U21(v0) -> null_U21 [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_U12, null_encode_isNat, null_encode_U21, null_encode_U31, null_encode_U41, null_encode_U42, null_encode_s, null_encode_plus, null_encode_0, null_s, null_U42, null_isNat, null_active, null_U41, null_plus, null_U12, null_U31, null_U21, null_U11, null_mark ---------------------------------------- (26) 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] U31(X1, c_active(X2)) -> U31(X1, X2) [1] mark(c_U31(X1, X2)) -> active(U31(mark(X1), X2)) [1] isNat(c_active(X)) -> isNat(X) [1] active(c_plus(N, c_s(M))) -> mark(U41(isNat(M), M, N)) [1] mark(c_U42(X1, X2, X3)) -> active(U42(mark(X1), X2, X3)) [1] U41(c_active(X1), X2, X3) -> U41(X1, X2, X3) [1] active(c_plus(N, 0)) -> mark(U31(isNat(N), N)) [1] mark(c_U11(X1, X2)) -> active(U11(mark(X1), X2)) [1] U42(X1, X2, c_active(X3)) -> U42(X1, X2, X3) [1] U11(X1, c_mark(X2)) -> U11(X1, X2) [1] U31(c_active(X1), X2) -> U31(X1, X2) [1] U41(X1, X2, c_mark(X3)) -> U41(X1, X2, X3) [1] active(c_U21(tt)) -> mark(tt) [1] active(c_isNat(c_s(V1))) -> mark(U21(isNat(V1))) [1] U42(X1, c_mark(X2), X3) -> U42(X1, X2, X3) [1] U31(X1, c_mark(X2)) -> U31(X1, X2) [1] U41(c_mark(X1), X2, X3) -> U41(X1, X2, X3) [1] U42(c_active(X1), X2, X3) -> U42(X1, X2, X3) [1] U12(c_mark(X)) -> U12(X) [1] U12(c_active(X)) -> U12(X) [1] U41(X1, c_active(X2), X3) -> U41(X1, X2, X3) [1] active(c_U12(tt)) -> mark(tt) [1] mark(c_U21(X)) -> active(U21(mark(X))) [1] U42(X1, c_active(X2), X3) -> U42(X1, X2, X3) [1] U41(X1, c_mark(X2), X3) -> U41(X1, X2, X3) [1] U31(c_mark(X1), X2) -> U31(X1, X2) [1] U42(c_mark(X1), X2, X3) -> U42(X1, X2, X3) [1] isNat(c_mark(X)) -> isNat(X) [1] U21(c_active(X)) -> U21(X) [1] active(c_isNat(0)) -> mark(tt) [1] U21(c_mark(X)) -> U21(X) [1] plus(X1, c_mark(X2)) -> plus(X1, X2) [1] mark(c_U12(X)) -> active(U12(mark(X))) [1] active(c_U11(tt, V2)) -> mark(U12(isNat(V2))) [1] active(c_U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) [1] U42(X1, X2, c_mark(X3)) -> U42(X1, X2, X3) [1] plus(c_active(X1), X2) -> plus(X1, X2) [1] mark(c_s(X)) -> active(s(mark(X))) [1] U41(X1, X2, c_active(X3)) -> U41(X1, X2, X3) [1] active(c_isNat(c_plus(V1, V2))) -> mark(U11(isNat(V1), V2)) [1] s(c_active(X)) -> s(X) [1] active(c_U42(tt, M, N)) -> mark(s(plus(N, M))) [1] s(c_mark(X)) -> s(X) [1] mark(c_U41(X1, X2, X3)) -> active(U41(mark(X1), X2, X3)) [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] active(c_U31(tt, N)) -> mark(N) [1] mark(c_isNat(X)) -> active(isNat(X)) [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] 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_U12(x_1)) -> U12(encArg(x_1)) [0] encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) [0] encArg(cons_U21(x_1)) -> U21(encArg(x_1)) [0] encArg(cons_U31(x_1, x_2)) -> U31(encArg(x_1), encArg(x_2)) [0] encArg(cons_U41(x_1, x_2, x_3)) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(cons_U42(x_1, x_2, x_3)) -> U42(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] 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_U12(x_1) -> U12(encArg(x_1)) [0] encode_isNat(x_1) -> isNat(encArg(x_1)) [0] encode_U21(x_1) -> U21(encArg(x_1)) [0] encode_U31(x_1, x_2) -> U31(encArg(x_1), encArg(x_2)) [0] encode_U41(x_1, x_2, x_3) -> U41(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_U42(x_1, x_2, x_3) -> U42(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_0 -> 0 [0] s(x0) -> c_s(x0) [0] U42(x0, x1, x2) -> c_U42(x0, x1, x2) [0] isNat(x0) -> c_isNat(x0) [0] active(x0) -> c_active(x0) [0] U41(x0, x1, x2) -> c_U41(x0, x1, x2) [0] plus(x0, x1) -> c_plus(x0, x1) [0] U12(x0) -> c_U12(x0) [0] U31(x0, x1) -> c_U31(x0, x1) [0] U21(x0) -> c_U21(x0) [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_U12(v0) -> null_encode_U12 [0] encode_isNat(v0) -> null_encode_isNat [0] encode_U21(v0) -> null_encode_U21 [0] encode_U31(v0, v1) -> null_encode_U31 [0] encode_U41(v0, v1, v2) -> null_encode_U41 [0] encode_U42(v0, v1, v2) -> null_encode_U42 [0] encode_s(v0) -> null_encode_s [0] encode_plus(v0, v1) -> null_encode_plus [0] encode_0 -> null_encode_0 [0] s(v0) -> null_s [0] U42(v0, v1, v2) -> null_U42 [0] isNat(v0) -> null_isNat [0] active(v0) -> null_active [0] U41(v0, v1, v2) -> null_U41 [0] plus(v0, v1) -> null_plus [0] U12(v0) -> null_U12 [0] U31(v0, v1) -> null_U31 [0] U21(v0) -> null_U21 [0] U11(v0, v1) -> null_U11 [0] mark(v0) -> null_mark [0] The TRS has the following type information: mark :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark tt :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark 0 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark -> tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark c_active :: 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tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_encode_U41 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_encode_U42 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_encode_s :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_encode_plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_encode_0 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_s :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U42 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_isNat :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_active :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U41 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_plus :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U12 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U31 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U21 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_U11 :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21:null_U11:null_mark null_mark :: tt:0:c_active:c_U31:c_s:c_plus:c_U42:c_U11:c_mark:c_U21:c_isNat:c_U12:c_U41:cons_active:cons_mark:cons_U11:cons_U12:cons_isNat:cons_U21:cons_U31:cons_U41:cons_U42:cons_s:cons_plus:null_encArg:null_encode_active:null_encode_U11:null_encode_tt:null_encode_mark:null_encode_U12:null_encode_isNat:null_encode_U21:null_encode_U31:null_encode_U41:null_encode_U42:null_encode_s:null_encode_plus:null_encode_0:null_s:null_U42:null_isNat:null_active:null_U41:null_plus:null_U12:null_U31:null_U21: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_U12 => 0 null_encode_isNat => 0 null_encode_U21 => 0 null_encode_U31 => 0 null_encode_U41 => 0 null_encode_U42 => 0 null_encode_s => 0 null_encode_plus => 0 null_encode_0 => 0 null_s => 0 null_U42 => 0 null_isNat => 0 null_active => 0 null_U41 => 0 null_plus => 0 null_U12 => 0 null_U31 => 0 null_U21 => 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 U12(z) -{ 1 }-> U12(X) :|: z = 1 + X, X >= 0 U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 U12(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 U21(z) -{ 1 }-> U21(X) :|: z = 1 + X, X >= 0 U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 U21(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 U31(z, z') -{ 1 }-> U31(X1, X2) :|: X1 >= 0, z' = 1 + X2, X2 >= 0, z = X1 U31(z, z') -{ 1 }-> U31(X1, X2) :|: X1 >= 0, z = 1 + X1, X2 >= 0, z' = X2 U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 U31(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 U41(z, z', z'') -{ 1 }-> U41(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U41(z, z', z'') -{ 1 }-> U41(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U41(z, z', z'') -{ 1 }-> U41(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U41(z, z', z'') -{ 0 }-> 1 + x0 + x1 + x2 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1, z'' = x2, x2 >= 0 U42(z, z', z'') -{ 1 }-> U42(X1, X2, X3) :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = 1 + X3 U42(z, z', z'') -{ 1 }-> U42(X1, X2, X3) :|: X1 >= 0, X3 >= 0, z' = 1 + X2, X2 >= 0, z = X1, z'' = X3 U42(z, z', z'') -{ 1 }-> U42(X1, X2, X3) :|: X1 >= 0, z = 1 + X1, X3 >= 0, X2 >= 0, z' = X2, z'' = X3 U42(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 U42(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(s(plus(N, M))) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(U42(isNat(N), M, N)) :|: z = 1 + 1 + M + N, M >= 0, N >= 0 active(z) -{ 1 }-> mark(U41(isNat(M), M, N)) :|: M >= 0, z = 1 + N + (1 + M), N >= 0 active(z) -{ 1 }-> mark(U31(isNat(N), N)) :|: z = 1 + N + 0, N >= 0 active(z) -{ 1 }-> mark(U21(isNat(V1))) :|: V1 >= 0, z = 1 + (1 + V1) active(z) -{ 1 }-> mark(U12(isNat(V2))) :|: z = 1 + 1 + V2, V2 >= 0 active(z) -{ 1 }-> mark(U11(isNat(V1), V2)) :|: V1 >= 0, V2 >= 0, z = 1 + (1 + V1 + V2) active(z) -{ 1 }-> mark(1) :|: z = 1 + 1 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 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 }-> active(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> U42(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 }-> U41(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 }-> U31(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> U21(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> U12(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 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_U12(z) -{ 0 }-> U12(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_U21(z) -{ 0 }-> U21(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_U31(z, z') -{ 0 }-> U31(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_U41(z, z', z'') -{ 0 }-> U41(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_U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_U42(z, z', z'') -{ 0 }-> U42(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_U42(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_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(U42(mark(X1), X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U41(mark(X1), X2, X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> active(U31(mark(X1), X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> active(U21(mark(X))) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> active(U12(mark(X))) :|: z = 1 + X, X >= 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. ---------------------------------------- (29) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (30) 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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) 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_U12(z0) -> U12(encArg(z0)) encode_isNat(z0) -> isNat(encArg(z0)) encode_U21(z0) -> U21(encArg(z0)) encode_U31(z0, z1) -> U31(encArg(z0), encArg(z1)) encode_U41(z0, z1, z2) -> U41(encArg(z0), encArg(z1), encArg(z2)) encode_U42(z0, z1, z2) -> U42(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c13(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1) -> c14(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_TT -> c15 ENCODE_MARK(z0) -> c16(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U12(z0) -> c17(U12'(encArg(z0)), ENCARG(z0)) ENCODE_ISNAT(z0) -> c18(ISNAT(encArg(z0)), ENCARG(z0)) ENCODE_U21(z0) -> c19(U21'(encArg(z0)), ENCARG(z0)) ENCODE_U31(z0, z1) -> c20(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_U41(z0, z1, z2) -> c21(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_U42(z0, z1, z2) -> c22(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c23(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c24(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_0 -> c25 ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), U12'(isNat(z0)), ISNAT(z0)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), U21'(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), U31'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c38(ACTIVE(tt)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c47(ACTIVE(0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) S tuples: ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), U12'(isNat(z0)), ISNAT(z0)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), U21'(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), U31'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c38(ACTIVE(tt)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c47(ACTIVE(0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U12_1, encode_isNat_1, encode_U21_1, encode_U31_2, encode_U41_3, encode_U42_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_TT, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCODE_0, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2 Compound Symbols: c, c1, c2_2, c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c13_2, c14_3, c15, c16_2, c17_2, c18_2, c19_2, c20_3, c21_4, c22_4, c23_2, c24_3, c25, c26_3, c27_1, c28_1, c29_1, c30_3, c31_3, c32_1, c33_3, c34_3, c35_3, c36_3, c37_3, c38_1, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1 ---------------------------------------- (31) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: ENCODE_0 -> c25 ENCARG(0) -> c1 ENCODE_TT -> c15 ENCARG(tt) -> c ---------------------------------------- (32) 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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) 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_U12(z0) -> U12(encArg(z0)) encode_isNat(z0) -> isNat(encArg(z0)) encode_U21(z0) -> U21(encArg(z0)) encode_U31(z0, z1) -> U31(encArg(z0), encArg(z1)) encode_U41(z0, z1, z2) -> U41(encArg(z0), encArg(z1), encArg(z2)) encode_U42(z0, z1, z2) -> U42(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c13(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1) -> c14(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MARK(z0) -> c16(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U12(z0) -> c17(U12'(encArg(z0)), ENCARG(z0)) ENCODE_ISNAT(z0) -> c18(ISNAT(encArg(z0)), ENCARG(z0)) ENCODE_U21(z0) -> c19(U21'(encArg(z0)), ENCARG(z0)) ENCODE_U31(z0, z1) -> c20(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_U41(z0, z1, z2) -> c21(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_U42(z0, z1, z2) -> c22(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c23(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c24(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), U12'(isNat(z0)), ISNAT(z0)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), U21'(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), U31'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c38(ACTIVE(tt)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c47(ACTIVE(0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) S tuples: ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), U12'(isNat(z0)), ISNAT(z0)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), S(plus(z1, z0)), PLUS(z1, z0)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), U21'(isNat(z0)), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), U31'(isNat(z0), z0), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(tt) -> c38(ACTIVE(tt)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) MARK(0) -> c47(ACTIVE(0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U12_1, encode_isNat_1, encode_U21_1, encode_U31_2, encode_U41_3, encode_U42_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2 Compound Symbols: c2_2, c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c13_2, c14_3, c16_2, c17_2, c18_2, c19_2, c20_3, c21_4, c22_4, c23_2, c24_3, c26_3, c27_1, c28_1, c29_1, c30_3, c31_3, c32_1, c33_3, c34_3, c35_3, c36_3, c37_3, c38_1, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c47_1, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (34) 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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) 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_U12(z0) -> U12(encArg(z0)) encode_isNat(z0) -> isNat(encArg(z0)) encode_U21(z0) -> U21(encArg(z0)) encode_U31(z0, z1) -> U31(encArg(z0), encArg(z1)) encode_U41(z0, z1, z2) -> U41(encArg(z0), encArg(z1), encArg(z2)) encode_U42(z0, z1, z2) -> U42(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_ACTIVE(z0) -> c13(ACTIVE(encArg(z0)), ENCARG(z0)) ENCODE_U11(z0, z1) -> c14(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_MARK(z0) -> c16(MARK(encArg(z0)), ENCARG(z0)) ENCODE_U12(z0) -> c17(U12'(encArg(z0)), ENCARG(z0)) ENCODE_ISNAT(z0) -> c18(ISNAT(encArg(z0)), ENCARG(z0)) ENCODE_U21(z0) -> c19(U21'(encArg(z0)), ENCARG(z0)) ENCODE_U31(z0, z1) -> c20(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_U41(z0, z1, z2) -> c21(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_U42(z0, z1, z2) -> c22(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCODE_S(z0) -> c23(S(encArg(z0)), ENCARG(z0)) ENCODE_PLUS(z0, z1) -> c24(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U12_1, encode_isNat_1, encode_U21_1, encode_U31_2, encode_U41_3, encode_U42_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2 Compound Symbols: c2_2, c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c13_2, c14_3, c16_2, c17_2, c18_2, c19_2, c20_3, c21_4, c22_4, c23_2, c24_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47 ---------------------------------------- (35) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) 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_U12(z0) -> U12(encArg(z0)) encode_isNat(z0) -> isNat(encArg(z0)) encode_U21(z0) -> U21(encArg(z0)) encode_U31(z0, z1) -> U31(encArg(z0), encArg(z1)) encode_U41(z0, z1, z2) -> U41(encArg(z0), encArg(z1), encArg(z2)) encode_U42(z0, z1, z2) -> U42(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_U12(z0) -> c(ENCARG(z0)) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_ISNAT(z0) -> c(ENCARG(z0)) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U21(z0) -> c(ENCARG(z0)) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U31(z0, z1) -> c(ENCARG(z0)) ENCODE_U31(z0, z1) -> c(ENCARG(z1)) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U41(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U41(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U41(z0, z1, z2) -> c(ENCARG(z2)) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U42(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U42(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)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U12_1, encode_isNat_1, encode_U21_1, encode_U31_2, encode_U41_3, encode_U42_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c2_2, c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1 ---------------------------------------- (37) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 18 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_U12(z0) -> c(ENCARG(z0)) ENCODE_ISNAT(z0) -> c(ENCARG(z0)) ENCODE_U21(z0) -> c(ENCARG(z0)) ENCODE_U31(z0, z1) -> c(ENCARG(z0)) ENCODE_U31(z0, z1) -> c(ENCARG(z1)) ENCODE_U41(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U41(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U41(z0, z1, z2) -> c(ENCARG(z2)) ENCODE_U42(z0, z1, z2) -> c(ENCARG(z0)) ENCODE_U42(z0, z1, z2) -> c(ENCARG(z1)) ENCODE_U42(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)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) 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_U12(z0) -> U12(encArg(z0)) encode_isNat(z0) -> isNat(encArg(z0)) encode_U21(z0) -> U21(encArg(z0)) encode_U31(z0, z1) -> U31(encArg(z0), encArg(z1)) encode_U41(z0, z1, z2) -> U41(encArg(z0), encArg(z1), encArg(z2)) encode_U42(z0, z1, z2) -> U42(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2, encArg_1, encode_active_1, encode_U11_2, encode_tt, encode_mark_1, encode_U12_1, encode_isNat_1, encode_U21_1, encode_U31_2, encode_U41_3, encode_U42_3, encode_s_1, encode_plus_2, encode_0 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c2_2, c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1 ---------------------------------------- (39) 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_U12(z0) -> U12(encArg(z0)) encode_isNat(z0) -> isNat(encArg(z0)) encode_U21(z0) -> U21(encArg(z0)) encode_U31(z0, z1) -> U31(encArg(z0), encArg(z1)) encode_U41(z0, z1, z2) -> U41(encArg(z0), encArg(z1), encArg(z2)) encode_U42(z0, z1, z2) -> U42(encArg(z0), encArg(z1), encArg(z2)) encode_s(z0) -> s(encArg(z0)) encode_plus(z0, z1) -> plus(encArg(z0), encArg(z1)) encode_0 -> 0 ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c2_2, c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1 ---------------------------------------- (41) 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_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(tt)) -> c2(ACTIVE(tt), ENCARG(tt)) ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2 ---------------------------------------- (43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(tt)) -> c2(ACTIVE(tt), ENCARG(tt)) ENCARG(cons_active(0)) -> c2(ACTIVE(0), ENCARG(0)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) 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_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c3_2, c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2 ---------------------------------------- (45) 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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U11(z0, z1)) -> c4(U11'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(tt)) -> c3(MARK(tt)) ENCARG(cons_mark(0)) -> c3(MARK(0)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c4_3, c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1 ---------------------------------------- (49) 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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c5_2, c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U12(z0)) -> c5(U12'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_U12(tt)) -> c5(U12'(tt), ENCARG(tt)) ENCARG(cons_U12(0)) -> c5(U12'(0), ENCARG(0)) ENCARG(cons_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(tt)) -> c5(U12'(tt), ENCARG(tt)) ENCARG(cons_U12(0)) -> c5(U12'(0), ENCARG(0)) ENCARG(cons_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2 ---------------------------------------- (55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_U12(0)) -> c5(U12'(0), ENCARG(0)) ENCARG(cons_U12(tt)) -> c5(U12'(tt), ENCARG(tt)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c6_2, c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_isNat(z0)) -> c6(ISNAT(encArg(z0)), ENCARG(z0)) by ENCARG(cons_isNat(tt)) -> c6(ISNAT(tt), ENCARG(tt)) ENCARG(cons_isNat(0)) -> c6(ISNAT(0), ENCARG(0)) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(tt)) -> c6(ISNAT(tt), ENCARG(tt)) ENCARG(cons_isNat(0)) -> c6(ISNAT(0), ENCARG(0)) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2 ---------------------------------------- (59) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_isNat(0)) -> c6(ISNAT(0), ENCARG(0)) ENCARG(cons_isNat(tt)) -> c6(ISNAT(tt), ENCARG(tt)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c7_2, c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U21(z0)) -> c7(U21'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_U21(tt)) -> c7(U21'(tt), ENCARG(tt)) ENCARG(cons_U21(0)) -> c7(U21'(0), ENCARG(0)) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(tt)) -> c7(U21'(tt), ENCARG(tt)) ENCARG(cons_U21(0)) -> c7(U21'(0), ENCARG(0)) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_U21(0)) -> c7(U21'(0), ENCARG(0)) ENCARG(cons_U21(tt)) -> c7(U21'(tt), ENCARG(tt)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c8_3, c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U31(z0, z1)) -> c8(U31'(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c9_4, c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U41(z0, z1, z2)) -> c9(U41'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) by ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c10_4, c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_U42(z0, z1, z2)) -> c10(U42'(encArg(z0), encArg(z1), encArg(z2)), ENCARG(z0), ENCARG(z1), ENCARG(z2)) by ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1), ENCARG(tt)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1), ENCARG(0)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(tt), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(0), ENCARG(x2)) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(tt), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(0), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c11_2, c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_s(z0)) -> c11(S(encArg(z0)), ENCARG(z0)) by ENCARG(cons_s(tt)) -> c11(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c11(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(tt)) -> c11(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c11(S(0), ENCARG(0)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_s(tt)) -> c11(S(tt), ENCARG(tt)) ENCARG(cons_s(0)) -> c11(S(0), ENCARG(0)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ENCARG_1, ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c12_3, c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_plus(z0, z1)) -> c12(PLUS(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0), ENCARG(tt)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0), ENCARG(0)) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(tt), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(0), ENCARG(x1)) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c37_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c37(ACTIVE(U11(mark(z0), z1)), U11'(mark(z0), z1), MARK(z0)) by MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c39_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U12(z0)) -> c39(ACTIVE(U12(mark(z0))), U12'(mark(z0)), MARK(z0)) by MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c41_3, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0)) -> c41(ACTIVE(U21(mark(z0))), U21'(mark(z0)), MARK(z0)) by MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c42_3, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c42(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0)) by MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c43_3, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) by MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c44_3, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(mark(z0), z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) by MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c45_3, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(s(z0)) -> c45(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0)) by MARK(s(z0)) -> c45(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(z0)) -> c45(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(z0)) -> c45(ACTIVE(s(z0)), S(mark(z0)), MARK(z0)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) K tuples:none Defined Rule Symbols: encArg_1, active_1, mark_1, U11_2, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c46_4, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c46(ACTIVE(plus(mark(z0), mark(z1))), PLUS(mark(z0), mark(z1)), MARK(z0), MARK(z1)) by MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (103) 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_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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)))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ENCODE_ACTIVE(0) -> c(ACTIVE(0)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_ACTIVE(tt) -> c(ACTIVE(tt)) ENCODE_ACTIVE(0) -> c(ACTIVE(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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U11(z0, z1) -> c(U11'(encArg(z0), encArg(z1))) ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (107) 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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_MARK(z0) -> c(MARK(encArg(z0))) ENCODE_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (109) 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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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)))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (111) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_MARK(tt) -> c(MARK(tt)) ENCODE_MARK(0) -> c(MARK(0)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U12(z0) -> c(U12'(encArg(z0))) ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U12(z0) -> c(U12'(encArg(z0))) by ENCODE_U12(tt) -> c(U12'(tt)) ENCODE_U12(0) -> c(U12'(0)) ENCODE_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(tt) -> c(U12'(tt)) ENCODE_U12(0) -> c(U12'(0)) ENCODE_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_U12(0) -> c(U12'(0)) ENCODE_U12(tt) -> c(U12'(tt)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_ISNAT(z0) -> c(ISNAT(encArg(z0))) ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (117) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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)))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_ISNAT(0) -> c(ISNAT(0)) ENCODE_ISNAT(tt) -> c(ISNAT(tt)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U21(z0) -> c(U21'(encArg(z0))) ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U21(z0) -> c(U21'(encArg(z0))) by ENCODE_U21(tt) -> c(U21'(tt)) ENCODE_U21(0) -> c(U21'(0)) ENCODE_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(tt) -> c(U21'(tt)) ENCODE_U21(0) -> c(U21'(0)) ENCODE_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_U21(tt) -> c(U21'(tt)) ENCODE_U21(0) -> c(U21'(0)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U31(z0, z1) -> c(U31'(encArg(z0), encArg(z1))) by ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U41(z0, z1, z2) -> c(U41'(encArg(z0), encArg(z1), encArg(z2))) by ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_U42(z0, z1, z2) -> c(U42'(encArg(z0), encArg(z1), encArg(z2))) by ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(tt) -> tt encArg(0) -> 0 encArg(cons_active(z0)) -> active(encArg(z0)) encArg(cons_mark(z0)) -> mark(encArg(z0)) encArg(cons_U11(z0, z1)) -> U11(encArg(z0), encArg(z1)) encArg(cons_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_S(z0) -> c(S(encArg(z0))) ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_S_1, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (131) 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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)))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_S(0) -> c(S(0)) ENCODE_S(tt) -> c(S(tt)) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCODE_PLUS(z0, z1) -> c(PLUS(encArg(z0), encArg(z1))) ENCARG(cons_active(cons_active(z0))) -> c2(ACTIVE(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_active(cons_mark(z0))) -> c2(ACTIVE(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCODE_PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c_1, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4 ---------------------------------------- (135) 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_U12(z0)) -> c(PLUS(encArg(x0), U12(encArg(z0)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) ENCODE_PLUS(x0, cons_U21(z0)) -> c(PLUS(encArg(x0), U21(encArg(z0)))) ENCODE_PLUS(x0, cons_U31(z0, z1)) -> c(PLUS(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U41(z0, z1, z2)) -> c(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U42(z0, z1, z2)) -> c(PLUS(encArg(x0), U42(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(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_U12(z0), x1) -> c(PLUS(U12(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U21(z0), x1) -> c(PLUS(U21(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U31(z0, z1), x1) -> c(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U41(z0, z1, z2), x1) -> c(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U42(z0, z1, z2), x1) -> c(PLUS(U42(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))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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_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_U12(z0)) -> c(PLUS(encArg(x0), U12(encArg(z0)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) ENCODE_PLUS(x0, cons_U21(z0)) -> c(PLUS(encArg(x0), U21(encArg(z0)))) ENCODE_PLUS(x0, cons_U31(z0, z1)) -> c(PLUS(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U41(z0, z1, z2)) -> c(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U42(z0, z1, z2)) -> c(PLUS(encArg(x0), U42(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(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_U12(z0), x1) -> c(PLUS(U12(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U21(z0), x1) -> c(PLUS(U21(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U31(z0, z1), x1) -> c(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U41(z0, z1, z2), x1) -> c(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U42(z0, z1, z2), x1) -> c(PLUS(U42(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))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4, c_1 ---------------------------------------- (137) 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_U12(z0)))) -> c2(ACTIVE(active(U12(encArg(z0)))), ENCARG(cons_active(cons_U12(z0)))) ENCARG(cons_active(cons_active(cons_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ENCARG(cons_active(cons_active(cons_U21(z0)))) -> c2(ACTIVE(active(U21(encArg(z0)))), ENCARG(cons_active(cons_U21(z0)))) ENCARG(cons_active(cons_active(cons_U31(z0, z1)))) -> c2(ACTIVE(active(U31(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U31(z0, z1)))) ENCARG(cons_active(cons_active(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(active(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(active(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U42(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)))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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_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_U12(z0)) -> c(PLUS(encArg(x0), U12(encArg(z0)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) ENCODE_PLUS(x0, cons_U21(z0)) -> c(PLUS(encArg(x0), U21(encArg(z0)))) ENCODE_PLUS(x0, cons_U31(z0, z1)) -> c(PLUS(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U41(z0, z1, z2)) -> c(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U42(z0, z1, z2)) -> c(PLUS(encArg(x0), U42(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(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_U12(z0), x1) -> c(PLUS(U12(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U21(z0), x1) -> c(PLUS(U21(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U31(z0, z1), x1) -> c(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U41(z0, z1, z2), x1) -> c(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U42(z0, z1, z2), x1) -> c(PLUS(U42(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))) 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_U12(z0)))) -> c2(ACTIVE(active(U12(encArg(z0)))), ENCARG(cons_active(cons_U12(z0)))) ENCARG(cons_active(cons_active(cons_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ENCARG(cons_active(cons_active(cons_U21(z0)))) -> c2(ACTIVE(active(U21(encArg(z0)))), ENCARG(cons_active(cons_U21(z0)))) ENCARG(cons_active(cons_active(cons_U31(z0, z1)))) -> c2(ACTIVE(active(U31(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U31(z0, z1)))) ENCARG(cons_active(cons_active(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(active(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(active(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4, c_1 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_active(cons_active(tt))) -> c2(ACTIVE(active(tt)), ENCARG(cons_active(tt))) ENCARG(cons_active(cons_active(0))) -> c2(ACTIVE(active(0)), ENCARG(cons_active(0))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 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_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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_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_U12(z0)) -> c(PLUS(encArg(x0), U12(encArg(z0)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) ENCODE_PLUS(x0, cons_U21(z0)) -> c(PLUS(encArg(x0), U21(encArg(z0)))) ENCODE_PLUS(x0, cons_U31(z0, z1)) -> c(PLUS(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U41(z0, z1, z2)) -> c(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U42(z0, z1, z2)) -> c(PLUS(encArg(x0), U42(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(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_U12(z0), x1) -> c(PLUS(U12(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U21(z0), x1) -> c(PLUS(U21(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U31(z0, z1), x1) -> c(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U41(z0, z1, z2), x1) -> c(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U42(z0, z1, z2), x1) -> c(PLUS(U42(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))) 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_U12(z0)))) -> c2(ACTIVE(active(U12(encArg(z0)))), ENCARG(cons_active(cons_U12(z0)))) ENCARG(cons_active(cons_active(cons_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ENCARG(cons_active(cons_active(cons_U21(z0)))) -> c2(ACTIVE(active(U21(encArg(z0)))), ENCARG(cons_active(cons_U21(z0)))) ENCARG(cons_active(cons_active(cons_U31(z0, z1)))) -> c2(ACTIVE(active(U31(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U31(z0, z1)))) ENCARG(cons_active(cons_active(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(active(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(active(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4, c_1 ---------------------------------------- (141) 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_U12(z0)))) -> c2(ACTIVE(mark(U12(encArg(z0)))), ENCARG(cons_mark(cons_U12(z0)))) 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(cons_U21(z0)))) -> c2(ACTIVE(mark(U21(encArg(z0)))), ENCARG(cons_mark(cons_U21(z0)))) ENCARG(cons_active(cons_mark(cons_U31(z0, z1)))) -> c2(ACTIVE(mark(U31(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U31(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(mark(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(mark(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U42(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)))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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_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_U12(z0)) -> c(PLUS(encArg(x0), U12(encArg(z0)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) ENCODE_PLUS(x0, cons_U21(z0)) -> c(PLUS(encArg(x0), U21(encArg(z0)))) ENCODE_PLUS(x0, cons_U31(z0, z1)) -> c(PLUS(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U41(z0, z1, z2)) -> c(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U42(z0, z1, z2)) -> c(PLUS(encArg(x0), U42(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(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_U12(z0), x1) -> c(PLUS(U12(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U21(z0), x1) -> c(PLUS(U21(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U31(z0, z1), x1) -> c(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U41(z0, z1, z2), x1) -> c(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U42(z0, z1, z2), x1) -> c(PLUS(U42(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))) 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_U12(z0)))) -> c2(ACTIVE(active(U12(encArg(z0)))), ENCARG(cons_active(cons_U12(z0)))) ENCARG(cons_active(cons_active(cons_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ENCARG(cons_active(cons_active(cons_U21(z0)))) -> c2(ACTIVE(active(U21(encArg(z0)))), ENCARG(cons_active(cons_U21(z0)))) ENCARG(cons_active(cons_active(cons_U31(z0, z1)))) -> c2(ACTIVE(active(U31(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U31(z0, z1)))) ENCARG(cons_active(cons_active(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(active(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(active(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U42(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_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_U12(z0)))) -> c2(ACTIVE(mark(U12(encArg(z0)))), ENCARG(cons_mark(cons_U12(z0)))) 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(cons_U21(z0)))) -> c2(ACTIVE(mark(U21(encArg(z0)))), ENCARG(cons_mark(cons_U21(z0)))) ENCARG(cons_active(cons_mark(cons_U31(z0, z1)))) -> c2(ACTIVE(mark(U31(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U31(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(mark(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(mark(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U42(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)))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4, c_1 ---------------------------------------- (143) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCARG(cons_active(cons_U11(z0, z1))) -> c2(ACTIVE(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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_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_U12(z0)) -> c(PLUS(encArg(x0), U12(encArg(z0)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) ENCODE_PLUS(x0, cons_U21(z0)) -> c(PLUS(encArg(x0), U21(encArg(z0)))) ENCODE_PLUS(x0, cons_U31(z0, z1)) -> c(PLUS(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U41(z0, z1, z2)) -> c(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U42(z0, z1, z2)) -> c(PLUS(encArg(x0), U42(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(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_U12(z0), x1) -> c(PLUS(U12(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U21(z0), x1) -> c(PLUS(U21(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U31(z0, z1), x1) -> c(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U41(z0, z1, z2), x1) -> c(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U42(z0, z1, z2), x1) -> c(PLUS(U42(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))) 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_U12(z0)))) -> c2(ACTIVE(active(U12(encArg(z0)))), ENCARG(cons_active(cons_U12(z0)))) ENCARG(cons_active(cons_active(cons_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ENCARG(cons_active(cons_active(cons_U21(z0)))) -> c2(ACTIVE(active(U21(encArg(z0)))), ENCARG(cons_active(cons_U21(z0)))) ENCARG(cons_active(cons_active(cons_U31(z0, z1)))) -> c2(ACTIVE(active(U31(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U31(z0, z1)))) ENCARG(cons_active(cons_active(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(active(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(active(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U42(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_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_U12(z0)))) -> c2(ACTIVE(mark(U12(encArg(z0)))), ENCARG(cons_mark(cons_U12(z0)))) 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(cons_U21(z0)))) -> c2(ACTIVE(mark(U21(encArg(z0)))), ENCARG(cons_mark(cons_U21(z0)))) ENCARG(cons_active(cons_mark(cons_U31(z0, z1)))) -> c2(ACTIVE(mark(U31(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U31(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(mark(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(mark(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U42(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(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(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4, c_1, c1_1 ---------------------------------------- (145) 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_U12(z0)))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0)))), ENCARG(cons_U11(x0, cons_U12(z0)))) 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(x0, cons_U21(z0)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0)))), ENCARG(cons_U11(x0, cons_U21(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U31(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U31(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U31(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U41(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_U42(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U42(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(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_U12(z0), x1))) -> c2(ACTIVE(U11(U12(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_U12(z0), 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_U11(cons_U21(z0), x1))) -> c2(ACTIVE(U11(U21(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0), x1))) ENCARG(cons_active(cons_U11(cons_U31(z0, z1), x1))) -> c2(ACTIVE(U11(U31(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U31(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U41(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U41(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_U42(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U42(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))) ---------------------------------------- (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_U12(z0)) -> U12(encArg(z0)) encArg(cons_isNat(z0)) -> isNat(encArg(z0)) encArg(cons_U21(z0)) -> U21(encArg(z0)) encArg(cons_U31(z0, z1)) -> U31(encArg(z0), encArg(z1)) encArg(cons_U41(z0, z1, z2)) -> U41(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_U42(z0, z1, z2)) -> U42(encArg(z0), encArg(z1), encArg(z2)) encArg(cons_s(z0)) -> s(encArg(z0)) encArg(cons_plus(z0, z1)) -> plus(encArg(z0), encArg(z1)) active(U11(tt, z0)) -> mark(U12(isNat(z0))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt, z0)) -> mark(z0) active(U41(tt, z0, z1)) -> mark(U42(isNat(z1), z0, z1)) active(U42(tt, z0, z1)) -> mark(s(plus(z1, z0))) active(isNat(0)) -> mark(tt) active(isNat(plus(z0, z1))) -> mark(U11(isNat(z0), z1)) active(isNat(s(z0))) -> mark(U21(isNat(z0))) active(plus(z0, 0)) -> mark(U31(isNat(z0), z0)) active(plus(z0, s(z1))) -> mark(U41(isNat(z1), z1, z0)) mark(U11(z0, z1)) -> active(U11(mark(z0), z1)) mark(tt) -> active(tt) mark(U12(z0)) -> active(U12(mark(z0))) mark(isNat(z0)) -> active(isNat(z0)) mark(U21(z0)) -> active(U21(mark(z0))) mark(U31(z0, z1)) -> active(U31(mark(z0), z1)) mark(U41(z0, z1, z2)) -> active(U41(mark(z0), z1, z2)) mark(U42(z0, z1, z2)) -> active(U42(mark(z0), z1, z2)) mark(s(z0)) -> active(s(mark(z0))) mark(plus(z0, z1)) -> active(plus(mark(z0), mark(z1))) 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) U12(mark(z0)) -> U12(z0) U12(active(z0)) -> U12(z0) isNat(mark(z0)) -> isNat(z0) isNat(active(z0)) -> isNat(z0) U21(mark(z0)) -> U21(z0) U21(active(z0)) -> U21(z0) U31(mark(z0), z1) -> U31(z0, z1) U31(z0, mark(z1)) -> U31(z0, z1) U31(active(z0), z1) -> U31(z0, z1) U31(z0, active(z1)) -> U31(z0, z1) U41(mark(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, mark(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, mark(z2)) -> U41(z0, z1, z2) U41(active(z0), z1, z2) -> U41(z0, z1, z2) U41(z0, active(z1), z2) -> U41(z0, z1, z2) U41(z0, z1, active(z2)) -> U41(z0, z1, z2) U42(mark(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, mark(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, mark(z2)) -> U42(z0, z1, z2) U42(active(z0), z1, z2) -> U42(z0, z1, z2) U42(z0, active(z1), z2) -> U42(z0, z1, z2) U42(z0, z1, active(z2)) -> U42(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) Tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 ENCARG(cons_active(cons_U12(z0))) -> c2(ACTIVE(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_active(cons_isNat(z0))) -> c2(ACTIVE(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_active(cons_U21(z0))) -> c2(ACTIVE(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_active(cons_U31(z0, z1))) -> c2(ACTIVE(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_active(cons_U41(z0, z1, z2))) -> c2(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_active(cons_U42(z0, z1, z2))) -> c2(ACTIVE(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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_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_U12(z0))) -> c3(MARK(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_mark(cons_isNat(z0))) -> c3(MARK(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_mark(cons_U21(z0))) -> c3(MARK(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_mark(cons_U31(z0, z1))) -> c3(MARK(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_mark(cons_U41(z0, z1, z2))) -> c3(MARK(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_mark(cons_U42(z0, z1, z2))) -> c3(MARK(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(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(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_U12(z0))) -> c4(U11'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U11(x0, cons_isNat(z0))) -> c4(U11'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U11(x0, cons_U21(z0))) -> c4(U11'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U11(x0, cons_U31(z0, z1))) -> c4(U11'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U11(x0, cons_U41(z0, z1, z2))) -> c4(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U11(x0, cons_U42(z0, z1, z2))) -> c4(U11'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(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(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_U12(z0), x1)) -> c4(U11'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), 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(cons_U21(z0), x1)) -> c4(U11'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U11(cons_U31(z0, z1), x1)) -> c4(U11'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U11(cons_U41(z0, z1, z2), x1)) -> c4(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U11(cons_U42(z0, z1, z2), x1)) -> c4(U11'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(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(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_U12(cons_active(z0))) -> c5(U12'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U12(cons_mark(z0))) -> c5(U12'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U12(cons_U11(z0, z1))) -> c5(U12'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U12(cons_U12(z0))) -> c5(U12'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U12(cons_isNat(z0))) -> c5(U12'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U12(cons_U21(z0))) -> c5(U12'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U12(cons_U31(z0, z1))) -> c5(U12'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U12(cons_U41(z0, z1, z2))) -> c5(U12'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U12(cons_U42(z0, z1, z2))) -> c5(U12'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U12(cons_s(z0))) -> c5(U12'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U12(cons_plus(z0, z1))) -> c5(U12'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_isNat(cons_active(z0))) -> c6(ISNAT(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_isNat(cons_mark(z0))) -> c6(ISNAT(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_isNat(cons_U11(z0, z1))) -> c6(ISNAT(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_isNat(cons_U12(z0))) -> c6(ISNAT(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_isNat(cons_isNat(z0))) -> c6(ISNAT(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_isNat(cons_U21(z0))) -> c6(ISNAT(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_isNat(cons_U31(z0, z1))) -> c6(ISNAT(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_isNat(cons_U41(z0, z1, z2))) -> c6(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_isNat(cons_U42(z0, z1, z2))) -> c6(ISNAT(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_isNat(cons_s(z0))) -> c6(ISNAT(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_isNat(cons_plus(z0, z1))) -> c6(ISNAT(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U21(cons_active(z0))) -> c7(U21'(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_U21(cons_mark(z0))) -> c7(U21'(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_U21(cons_U11(z0, z1))) -> c7(U21'(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U21(cons_U12(z0))) -> c7(U21'(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_U21(cons_isNat(z0))) -> c7(U21'(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_U21(cons_U21(z0))) -> c7(U21'(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_U21(cons_U31(z0, z1))) -> c7(U21'(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U21(cons_U41(z0, z1, z2))) -> c7(U21'(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U21(cons_U42(z0, z1, z2))) -> c7(U21'(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U21(cons_s(z0))) -> c7(U21'(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_U21(cons_plus(z0, z1))) -> c7(U21'(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(x0, cons_active(z0))) -> c8(U31'(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_U31(x0, cons_mark(z0))) -> c8(U31'(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_U31(x0, cons_U11(z0, z1))) -> c8(U31'(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U31(x0, cons_U12(z0))) -> c8(U31'(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_U31(x0, cons_isNat(z0))) -> c8(U31'(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_U31(x0, cons_U21(z0))) -> c8(U31'(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_U31(x0, cons_U31(z0, z1))) -> c8(U31'(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U31(x0, cons_U41(z0, z1, z2))) -> c8(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U31(x0, cons_U42(z0, z1, z2))) -> c8(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U31(x0, cons_s(z0))) -> c8(U31'(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_U31(x0, cons_plus(z0, z1))) -> c8(U31'(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U31(cons_active(z0), x1)) -> c8(U31'(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_mark(z0), x1)) -> c8(U31'(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U11(z0, z1), x1)) -> c8(U31'(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U12(z0), x1)) -> c8(U31'(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_isNat(z0), x1)) -> c8(U31'(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U21(z0), x1)) -> c8(U31'(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_U31(z0, z1), x1)) -> c8(U31'(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(cons_U41(z0, z1, z2), x1)) -> c8(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_U42(z0, z1, z2), x1)) -> c8(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_U31(cons_s(z0), x1)) -> c8(U31'(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_U31(cons_plus(z0, z1), x1)) -> c8(U31'(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_U31(x0, tt)) -> c8(U31'(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_U31(x0, 0)) -> c8(U31'(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_U31(tt, x1)) -> c8(U31'(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_U31(0, x1)) -> c8(U31'(0, encArg(x1)), ENCARG(x1)) ENCARG(cons_U41(x0, x1, cons_active(z0))) -> c9(U41'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U41(x0, x1, cons_mark(z0))) -> c9(U41'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U41(x0, x1, cons_U11(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U12(z0))) -> c9(U41'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U41(x0, x1, cons_isNat(z0))) -> c9(U41'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U41(x0, x1, cons_U21(z0))) -> c9(U41'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U41(x0, x1, cons_U31(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U41(x0, x1, cons_U41(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_U42(z0, z1, z2))) -> c9(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U41(x0, x1, cons_s(z0))) -> c9(U41'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U41(x0, x1, cons_plus(z0, z1))) -> c9(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U41(x0, cons_active(z0), x2)) -> c9(U41'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_mark(z0), x2)) -> c9(U41'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U11(z0, z1), x2)) -> c9(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U12(z0), x2)) -> c9(U41'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_isNat(z0), x2)) -> c9(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U21(z0), x2)) -> c9(U41'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U31(z0, z1), x2)) -> c9(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U41(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_U42(z0, z1, z2), x2)) -> c9(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_s(z0), x2)) -> c9(U41'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U41(x0, cons_plus(z0, z1), x2)) -> c9(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U41(cons_active(z0), x1, x2)) -> c9(U41'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_mark(z0), x1, x2)) -> c9(U41'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U11(z0, z1), x1, x2)) -> c9(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U12(z0), x1, x2)) -> c9(U41'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_isNat(z0), x1, x2)) -> c9(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U21(z0), x1, x2)) -> c9(U41'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U31(z0, z1), x1, x2)) -> c9(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U41(z0, z1, z2), x1, x2)) -> c9(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_U42(z0, z1, z2), x1, x2)) -> c9(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_s(z0), x1, x2)) -> c9(U41'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(cons_plus(z0, z1), x1, x2)) -> c9(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(x0, x1, tt)) -> c9(U41'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, x1, 0)) -> c9(U41'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U41(x0, tt, x2)) -> c9(U41'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(x0, 0, x2)) -> c9(U41'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U41(tt, x1, x2)) -> c9(U41'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U41(0, x1, x2)) -> c9(U41'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, cons_active(z0))) -> c10(U42'(encArg(x0), encArg(x1), active(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_active(z0))) ENCARG(cons_U42(x0, x1, cons_mark(z0))) -> c10(U42'(encArg(x0), encArg(x1), mark(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_mark(z0))) ENCARG(cons_U42(x0, x1, cons_U11(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U11(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U12(z0))) -> c10(U42'(encArg(x0), encArg(x1), U12(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U12(z0))) ENCARG(cons_U42(x0, x1, cons_isNat(z0))) -> c10(U42'(encArg(x0), encArg(x1), isNat(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_isNat(z0))) ENCARG(cons_U42(x0, x1, cons_U21(z0))) -> c10(U42'(encArg(x0), encArg(x1), U21(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U21(z0))) ENCARG(cons_U42(x0, x1, cons_U31(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U31(z0, z1))) ENCARG(cons_U42(x0, x1, cons_U41(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_U42(z0, z1, z2))) -> c10(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(x1), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_U42(x0, x1, cons_s(z0))) -> c10(U42'(encArg(x0), encArg(x1), s(encArg(z0))), ENCARG(x0), ENCARG(x1), ENCARG(cons_s(z0))) ENCARG(cons_U42(x0, x1, cons_plus(z0, z1))) -> c10(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(x1), ENCARG(cons_plus(z0, z1))) ENCARG(cons_U42(x0, cons_active(z0), x2)) -> c10(U42'(encArg(x0), active(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_active(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_mark(z0), x2)) -> c10(U42'(encArg(x0), mark(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_mark(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U11(z0, z1), x2)) -> c10(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U11(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U12(z0), x2)) -> c10(U42'(encArg(x0), U12(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U12(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_isNat(z0), x2)) -> c10(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_isNat(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U21(z0), x2)) -> c10(U42'(encArg(x0), U21(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_U21(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U31(z0, z1), x2)) -> c10(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_U31(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U41(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_U42(z0, z1, z2), x2)) -> c10(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2)), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_s(z0), x2)) -> c10(U42'(encArg(x0), s(encArg(z0)), encArg(x2)), ENCARG(x0), ENCARG(cons_s(z0)), ENCARG(x2)) ENCARG(cons_U42(x0, cons_plus(z0, z1), x2)) -> c10(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2)), ENCARG(x0), ENCARG(cons_plus(z0, z1)), ENCARG(x2)) ENCARG(cons_U42(cons_active(z0), x1, x2)) -> c10(U42'(active(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_active(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_mark(z0), x1, x2)) -> c10(U42'(mark(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_mark(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U11(z0, z1), x1, x2)) -> c10(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U11(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U12(z0), x1, x2)) -> c10(U42'(U12(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U12(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_isNat(z0), x1, x2)) -> c10(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_isNat(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U21(z0), x1, x2)) -> c10(U42'(U21(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_U21(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U31(z0, z1), x1, x2)) -> c10(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_U31(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U41(z0, z1, z2), x1, x2)) -> c10(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_U42(z0, z1, z2), x1, x2)) -> c10(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_s(z0), x1, x2)) -> c10(U42'(s(encArg(z0)), encArg(x1), encArg(x2)), ENCARG(cons_s(z0)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(cons_plus(z0, z1), x1, x2)) -> c10(U42'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2)), ENCARG(cons_plus(z0, z1)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(x0, x1, tt)) -> c10(U42'(encArg(x0), encArg(x1), tt), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, x1, 0)) -> c10(U42'(encArg(x0), encArg(x1), 0), ENCARG(x0), ENCARG(x1)) ENCARG(cons_U42(x0, tt, x2)) -> c10(U42'(encArg(x0), tt, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(x0, 0, x2)) -> c10(U42'(encArg(x0), 0, encArg(x2)), ENCARG(x0), ENCARG(x2)) ENCARG(cons_U42(tt, x1, x2)) -> c10(U42'(tt, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_U42(0, x1, x2)) -> c10(U42'(0, encArg(x1), encArg(x2)), ENCARG(x1), ENCARG(x2)) ENCARG(cons_s(cons_active(z0))) -> c11(S(active(encArg(z0))), ENCARG(cons_active(z0))) ENCARG(cons_s(cons_mark(z0))) -> c11(S(mark(encArg(z0))), ENCARG(cons_mark(z0))) ENCARG(cons_s(cons_U11(z0, z1))) -> c11(S(U11(encArg(z0), encArg(z1))), ENCARG(cons_U11(z0, z1))) ENCARG(cons_s(cons_U12(z0))) -> c11(S(U12(encArg(z0))), ENCARG(cons_U12(z0))) ENCARG(cons_s(cons_isNat(z0))) -> c11(S(isNat(encArg(z0))), ENCARG(cons_isNat(z0))) ENCARG(cons_s(cons_U21(z0))) -> c11(S(U21(encArg(z0))), ENCARG(cons_U21(z0))) ENCARG(cons_s(cons_U31(z0, z1))) -> c11(S(U31(encArg(z0), encArg(z1))), ENCARG(cons_U31(z0, z1))) ENCARG(cons_s(cons_U41(z0, z1, z2))) -> c11(S(U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_s(cons_U42(z0, z1, z2))) -> c11(S(U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_s(cons_s(z0))) -> c11(S(s(encArg(z0))), ENCARG(cons_s(z0))) ENCARG(cons_s(cons_plus(z0, z1))) -> c11(S(plus(encArg(z0), encArg(z1))), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(x0, cons_active(z0))) -> c12(PLUS(encArg(x0), active(encArg(z0))), ENCARG(x0), ENCARG(cons_active(z0))) ENCARG(cons_plus(x0, cons_mark(z0))) -> c12(PLUS(encArg(x0), mark(encArg(z0))), ENCARG(x0), ENCARG(cons_mark(z0))) ENCARG(cons_plus(x0, cons_U11(z0, z1))) -> c12(PLUS(encArg(x0), U11(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U11(z0, z1))) ENCARG(cons_plus(x0, cons_U12(z0))) -> c12(PLUS(encArg(x0), U12(encArg(z0))), ENCARG(x0), ENCARG(cons_U12(z0))) ENCARG(cons_plus(x0, cons_isNat(z0))) -> c12(PLUS(encArg(x0), isNat(encArg(z0))), ENCARG(x0), ENCARG(cons_isNat(z0))) ENCARG(cons_plus(x0, cons_U21(z0))) -> c12(PLUS(encArg(x0), U21(encArg(z0))), ENCARG(x0), ENCARG(cons_U21(z0))) ENCARG(cons_plus(x0, cons_U31(z0, z1))) -> c12(PLUS(encArg(x0), U31(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_U31(z0, z1))) ENCARG(cons_plus(x0, cons_U41(z0, z1, z2))) -> c12(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U41(z0, z1, z2))) ENCARG(cons_plus(x0, cons_U42(z0, z1, z2))) -> c12(PLUS(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2))), ENCARG(x0), ENCARG(cons_U42(z0, z1, z2))) ENCARG(cons_plus(x0, cons_s(z0))) -> c12(PLUS(encArg(x0), s(encArg(z0))), ENCARG(x0), ENCARG(cons_s(z0))) ENCARG(cons_plus(x0, cons_plus(z0, z1))) -> c12(PLUS(encArg(x0), plus(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_plus(z0, z1))) ENCARG(cons_plus(cons_active(z0), x1)) -> c12(PLUS(active(encArg(z0)), encArg(x1)), ENCARG(cons_active(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_mark(z0), x1)) -> c12(PLUS(mark(encArg(z0)), encArg(x1)), ENCARG(cons_mark(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U11(z0, z1), x1)) -> c12(PLUS(U11(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U11(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U12(z0), x1)) -> c12(PLUS(U12(encArg(z0)), encArg(x1)), ENCARG(cons_U12(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_isNat(z0), x1)) -> c12(PLUS(isNat(encArg(z0)), encArg(x1)), ENCARG(cons_isNat(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U21(z0), x1)) -> c12(PLUS(U21(encArg(z0)), encArg(x1)), ENCARG(cons_U21(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_U31(z0, z1), x1)) -> c12(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_U31(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(cons_U41(z0, z1, z2), x1)) -> c12(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U41(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_U42(z0, z1, z2), x1)) -> c12(PLUS(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1)), ENCARG(cons_U42(z0, z1, z2)), ENCARG(x1)) ENCARG(cons_plus(cons_s(z0), x1)) -> c12(PLUS(s(encArg(z0)), encArg(x1)), ENCARG(cons_s(z0)), ENCARG(x1)) ENCARG(cons_plus(cons_plus(z0, z1), x1)) -> c12(PLUS(plus(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_plus(z0, z1)), ENCARG(x1)) ENCARG(cons_plus(x0, tt)) -> c12(PLUS(encArg(x0), tt), ENCARG(x0)) ENCARG(cons_plus(x0, 0)) -> c12(PLUS(encArg(x0), 0), ENCARG(x0)) ENCARG(cons_plus(tt, x1)) -> c12(PLUS(tt, encArg(x1)), ENCARG(x1)) ENCARG(cons_plus(0, x1)) -> c12(PLUS(0, encArg(x1)), ENCARG(x1)) MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(ACTIVE(plus(active(0), mark(x1))), PLUS(mark(0), mark(x1)), MARK(0), MARK(x1)) ENCODE_ACTIVE(cons_active(z0)) -> c(ACTIVE(active(encArg(z0)))) ENCODE_ACTIVE(cons_mark(z0)) -> c(ACTIVE(mark(encArg(z0)))) ENCODE_ACTIVE(cons_U11(z0, z1)) -> c(ACTIVE(U11(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U12(z0)) -> c(ACTIVE(U12(encArg(z0)))) ENCODE_ACTIVE(cons_isNat(z0)) -> c(ACTIVE(isNat(encArg(z0)))) ENCODE_ACTIVE(cons_U21(z0)) -> c(ACTIVE(U21(encArg(z0)))) ENCODE_ACTIVE(cons_U31(z0, z1)) -> c(ACTIVE(U31(encArg(z0), encArg(z1)))) ENCODE_ACTIVE(cons_U41(z0, z1, z2)) -> c(ACTIVE(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ACTIVE(cons_U42(z0, z1, z2)) -> c(ACTIVE(U42(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_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_U12(z0)) -> c(U11'(encArg(x0), U12(encArg(z0)))) ENCODE_U11(x0, cons_isNat(z0)) -> c(U11'(encArg(x0), isNat(encArg(z0)))) ENCODE_U11(x0, cons_U21(z0)) -> c(U11'(encArg(x0), U21(encArg(z0)))) ENCODE_U11(x0, cons_U31(z0, z1)) -> c(U11'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U11(x0, cons_U41(z0, z1, z2)) -> c(U11'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U11(x0, cons_U42(z0, z1, z2)) -> c(U11'(encArg(x0), U42(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(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_U12(z0), x1) -> c(U11'(U12(encArg(z0)), encArg(x1))) ENCODE_U11(cons_isNat(z0), x1) -> c(U11'(isNat(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U21(z0), x1) -> c(U11'(U21(encArg(z0)), encArg(x1))) ENCODE_U11(cons_U31(z0, z1), x1) -> c(U11'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U11(cons_U41(z0, z1, z2), x1) -> c(U11'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U11(cons_U42(z0, z1, z2), x1) -> c(U11'(U42(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_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_U12(z0)) -> c(MARK(U12(encArg(z0)))) ENCODE_MARK(cons_isNat(z0)) -> c(MARK(isNat(encArg(z0)))) ENCODE_MARK(cons_U21(z0)) -> c(MARK(U21(encArg(z0)))) ENCODE_MARK(cons_U31(z0, z1)) -> c(MARK(U31(encArg(z0), encArg(z1)))) ENCODE_MARK(cons_U41(z0, z1, z2)) -> c(MARK(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_MARK(cons_U42(z0, z1, z2)) -> c(MARK(U42(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_U12(cons_active(z0)) -> c(U12'(active(encArg(z0)))) ENCODE_U12(cons_mark(z0)) -> c(U12'(mark(encArg(z0)))) ENCODE_U12(cons_U11(z0, z1)) -> c(U12'(U11(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U12(z0)) -> c(U12'(U12(encArg(z0)))) ENCODE_U12(cons_isNat(z0)) -> c(U12'(isNat(encArg(z0)))) ENCODE_U12(cons_U21(z0)) -> c(U12'(U21(encArg(z0)))) ENCODE_U12(cons_U31(z0, z1)) -> c(U12'(U31(encArg(z0), encArg(z1)))) ENCODE_U12(cons_U41(z0, z1, z2)) -> c(U12'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_U42(z0, z1, z2)) -> c(U12'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U12(cons_s(z0)) -> c(U12'(s(encArg(z0)))) ENCODE_U12(cons_plus(z0, z1)) -> c(U12'(plus(encArg(z0), encArg(z1)))) 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_U12(z0)) -> c(ISNAT(U12(encArg(z0)))) ENCODE_ISNAT(cons_isNat(z0)) -> c(ISNAT(isNat(encArg(z0)))) ENCODE_ISNAT(cons_U21(z0)) -> c(ISNAT(U21(encArg(z0)))) ENCODE_ISNAT(cons_U31(z0, z1)) -> c(ISNAT(U31(encArg(z0), encArg(z1)))) ENCODE_ISNAT(cons_U41(z0, z1, z2)) -> c(ISNAT(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_ISNAT(cons_U42(z0, z1, z2)) -> c(ISNAT(U42(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_U21(cons_active(z0)) -> c(U21'(active(encArg(z0)))) ENCODE_U21(cons_mark(z0)) -> c(U21'(mark(encArg(z0)))) ENCODE_U21(cons_U11(z0, z1)) -> c(U21'(U11(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U12(z0)) -> c(U21'(U12(encArg(z0)))) ENCODE_U21(cons_isNat(z0)) -> c(U21'(isNat(encArg(z0)))) ENCODE_U21(cons_U21(z0)) -> c(U21'(U21(encArg(z0)))) ENCODE_U21(cons_U31(z0, z1)) -> c(U21'(U31(encArg(z0), encArg(z1)))) ENCODE_U21(cons_U41(z0, z1, z2)) -> c(U21'(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_U42(z0, z1, z2)) -> c(U21'(U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U21(cons_s(z0)) -> c(U21'(s(encArg(z0)))) ENCODE_U21(cons_plus(z0, z1)) -> c(U21'(plus(encArg(z0), encArg(z1)))) ENCODE_U31(x0, tt) -> c(U31'(encArg(x0), tt)) ENCODE_U31(x0, 0) -> c(U31'(encArg(x0), 0)) ENCODE_U31(x0, cons_active(z0)) -> c(U31'(encArg(x0), active(encArg(z0)))) ENCODE_U31(x0, cons_mark(z0)) -> c(U31'(encArg(x0), mark(encArg(z0)))) ENCODE_U31(x0, cons_U11(z0, z1)) -> c(U31'(encArg(x0), U11(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U12(z0)) -> c(U31'(encArg(x0), U12(encArg(z0)))) ENCODE_U31(x0, cons_isNat(z0)) -> c(U31'(encArg(x0), isNat(encArg(z0)))) ENCODE_U31(x0, cons_U21(z0)) -> c(U31'(encArg(x0), U21(encArg(z0)))) ENCODE_U31(x0, cons_U31(z0, z1)) -> c(U31'(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_U31(x0, cons_U41(z0, z1, z2)) -> c(U31'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_U42(z0, z1, z2)) -> c(U31'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U31(x0, cons_s(z0)) -> c(U31'(encArg(x0), s(encArg(z0)))) ENCODE_U31(x0, cons_plus(z0, z1)) -> c(U31'(encArg(x0), plus(encArg(z0), encArg(z1)))) ENCODE_U31(tt, x1) -> c(U31'(tt, encArg(x1))) ENCODE_U31(0, x1) -> c(U31'(0, encArg(x1))) ENCODE_U31(cons_active(z0), x1) -> c(U31'(active(encArg(z0)), encArg(x1))) ENCODE_U31(cons_mark(z0), x1) -> c(U31'(mark(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U11(z0, z1), x1) -> c(U31'(U11(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U12(z0), x1) -> c(U31'(U12(encArg(z0)), encArg(x1))) ENCODE_U31(cons_isNat(z0), x1) -> c(U31'(isNat(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U21(z0), x1) -> c(U31'(U21(encArg(z0)), encArg(x1))) ENCODE_U31(cons_U31(z0, z1), x1) -> c(U31'(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U31(cons_U41(z0, z1, z2), x1) -> c(U31'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_U42(z0, z1, z2), x1) -> c(U31'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_U31(cons_s(z0), x1) -> c(U31'(s(encArg(z0)), encArg(x1))) ENCODE_U31(cons_plus(z0, z1), x1) -> c(U31'(plus(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_U41(x0, x1, tt) -> c(U41'(encArg(x0), encArg(x1), tt)) ENCODE_U41(x0, x1, 0) -> c(U41'(encArg(x0), encArg(x1), 0)) ENCODE_U41(x0, x1, cons_active(z0)) -> c(U41'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U41(x0, x1, cons_mark(z0)) -> c(U41'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U41(x0, x1, cons_U11(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U12(z0)) -> c(U41'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U41(x0, x1, cons_isNat(z0)) -> c(U41'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U41(x0, x1, cons_U21(z0)) -> c(U41'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U41(x0, x1, cons_U31(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U41(x0, x1, cons_U41(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_U42(z0, z1, z2)) -> c(U41'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U41(x0, x1, cons_s(z0)) -> c(U41'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U41(x0, x1, cons_plus(z0, z1)) -> c(U41'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U41(x0, tt, x2) -> c(U41'(encArg(x0), tt, encArg(x2))) ENCODE_U41(x0, 0, x2) -> c(U41'(encArg(x0), 0, encArg(x2))) ENCODE_U41(x0, cons_active(z0), x2) -> c(U41'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_mark(z0), x2) -> c(U41'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U11(z0, z1), x2) -> c(U41'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U12(z0), x2) -> c(U41'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_isNat(z0), x2) -> c(U41'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U21(z0), x2) -> c(U41'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_U31(z0, z1), x2) -> c(U41'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(x0, cons_U41(z0, z1, z2), x2) -> c(U41'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_U42(z0, z1, z2), x2) -> c(U41'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U41(x0, cons_s(z0), x2) -> c(U41'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U41(x0, cons_plus(z0, z1), x2) -> c(U41'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U41(tt, x1, x2) -> c(U41'(tt, encArg(x1), encArg(x2))) ENCODE_U41(0, x1, x2) -> c(U41'(0, encArg(x1), encArg(x2))) ENCODE_U41(cons_active(z0), x1, x2) -> c(U41'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_mark(z0), x1, x2) -> c(U41'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U11(z0, z1), x1, x2) -> c(U41'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U12(z0), x1, x2) -> c(U41'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_isNat(z0), x1, x2) -> c(U41'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U21(z0), x1, x2) -> c(U41'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U31(z0, z1), x1, x2) -> c(U41'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U41(z0, z1, z2), x1, x2) -> c(U41'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_U42(z0, z1, z2), x1, x2) -> c(U41'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U41(cons_s(z0), x1, x2) -> c(U41'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U41(cons_plus(z0, z1), x1, x2) -> c(U41'(plus(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(x0, x1, tt) -> c(U42'(encArg(x0), encArg(x1), tt)) ENCODE_U42(x0, x1, 0) -> c(U42'(encArg(x0), encArg(x1), 0)) ENCODE_U42(x0, x1, cons_active(z0)) -> c(U42'(encArg(x0), encArg(x1), active(encArg(z0)))) ENCODE_U42(x0, x1, cons_mark(z0)) -> c(U42'(encArg(x0), encArg(x1), mark(encArg(z0)))) ENCODE_U42(x0, x1, cons_U11(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U11(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U12(z0)) -> c(U42'(encArg(x0), encArg(x1), U12(encArg(z0)))) ENCODE_U42(x0, x1, cons_isNat(z0)) -> c(U42'(encArg(x0), encArg(x1), isNat(encArg(z0)))) ENCODE_U42(x0, x1, cons_U21(z0)) -> c(U42'(encArg(x0), encArg(x1), U21(encArg(z0)))) ENCODE_U42(x0, x1, cons_U31(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), U31(encArg(z0), encArg(z1)))) ENCODE_U42(x0, x1, cons_U41(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_U42(z0, z1, z2)) -> c(U42'(encArg(x0), encArg(x1), U42(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_U42(x0, x1, cons_s(z0)) -> c(U42'(encArg(x0), encArg(x1), s(encArg(z0)))) ENCODE_U42(x0, x1, cons_plus(z0, z1)) -> c(U42'(encArg(x0), encArg(x1), plus(encArg(z0), encArg(z1)))) ENCODE_U42(x0, tt, x2) -> c(U42'(encArg(x0), tt, encArg(x2))) ENCODE_U42(x0, 0, x2) -> c(U42'(encArg(x0), 0, encArg(x2))) ENCODE_U42(x0, cons_active(z0), x2) -> c(U42'(encArg(x0), active(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_mark(z0), x2) -> c(U42'(encArg(x0), mark(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U11(z0, z1), x2) -> c(U42'(encArg(x0), U11(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U12(z0), x2) -> c(U42'(encArg(x0), U12(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_isNat(z0), x2) -> c(U42'(encArg(x0), isNat(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U21(z0), x2) -> c(U42'(encArg(x0), U21(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_U31(z0, z1), x2) -> c(U42'(encArg(x0), U31(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(x0, cons_U41(z0, z1, z2), x2) -> c(U42'(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_U42(z0, z1, z2), x2) -> c(U42'(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x2))) ENCODE_U42(x0, cons_s(z0), x2) -> c(U42'(encArg(x0), s(encArg(z0)), encArg(x2))) ENCODE_U42(x0, cons_plus(z0, z1), x2) -> c(U42'(encArg(x0), plus(encArg(z0), encArg(z1)), encArg(x2))) ENCODE_U42(tt, x1, x2) -> c(U42'(tt, encArg(x1), encArg(x2))) ENCODE_U42(0, x1, x2) -> c(U42'(0, encArg(x1), encArg(x2))) ENCODE_U42(cons_active(z0), x1, x2) -> c(U42'(active(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_mark(z0), x1, x2) -> c(U42'(mark(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U11(z0, z1), x1, x2) -> c(U42'(U11(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U12(z0), x1, x2) -> c(U42'(U12(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_isNat(z0), x1, x2) -> c(U42'(isNat(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U21(z0), x1, x2) -> c(U42'(U21(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U31(z0, z1), x1, x2) -> c(U42'(U31(encArg(z0), encArg(z1)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U41(z0, z1, z2), x1, x2) -> c(U42'(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_U42(z0, z1, z2), x1, x2) -> c(U42'(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1), encArg(x2))) ENCODE_U42(cons_s(z0), x1, x2) -> c(U42'(s(encArg(z0)), encArg(x1), encArg(x2))) ENCODE_U42(cons_plus(z0, z1), x1, x2) -> c(U42'(plus(encArg(z0), encArg(z1)), 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_U12(z0)) -> c(S(U12(encArg(z0)))) ENCODE_S(cons_isNat(z0)) -> c(S(isNat(encArg(z0)))) ENCODE_S(cons_U21(z0)) -> c(S(U21(encArg(z0)))) ENCODE_S(cons_U31(z0, z1)) -> c(S(U31(encArg(z0), encArg(z1)))) ENCODE_S(cons_U41(z0, z1, z2)) -> c(S(U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_S(cons_U42(z0, z1, z2)) -> c(S(U42(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_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_U12(z0)) -> c(PLUS(encArg(x0), U12(encArg(z0)))) ENCODE_PLUS(x0, cons_isNat(z0)) -> c(PLUS(encArg(x0), isNat(encArg(z0)))) ENCODE_PLUS(x0, cons_U21(z0)) -> c(PLUS(encArg(x0), U21(encArg(z0)))) ENCODE_PLUS(x0, cons_U31(z0, z1)) -> c(PLUS(encArg(x0), U31(encArg(z0), encArg(z1)))) ENCODE_PLUS(x0, cons_U41(z0, z1, z2)) -> c(PLUS(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))) ENCODE_PLUS(x0, cons_U42(z0, z1, z2)) -> c(PLUS(encArg(x0), U42(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(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_U12(z0), x1) -> c(PLUS(U12(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_isNat(z0), x1) -> c(PLUS(isNat(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U21(z0), x1) -> c(PLUS(U21(encArg(z0)), encArg(x1))) ENCODE_PLUS(cons_U31(z0, z1), x1) -> c(PLUS(U31(encArg(z0), encArg(z1)), encArg(x1))) ENCODE_PLUS(cons_U41(z0, z1, z2), x1) -> c(PLUS(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))) ENCODE_PLUS(cons_U42(z0, z1, z2), x1) -> c(PLUS(U42(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))) 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_U12(z0)))) -> c2(ACTIVE(active(U12(encArg(z0)))), ENCARG(cons_active(cons_U12(z0)))) ENCARG(cons_active(cons_active(cons_isNat(z0)))) -> c2(ACTIVE(active(isNat(encArg(z0)))), ENCARG(cons_active(cons_isNat(z0)))) ENCARG(cons_active(cons_active(cons_U21(z0)))) -> c2(ACTIVE(active(U21(encArg(z0)))), ENCARG(cons_active(cons_U21(z0)))) ENCARG(cons_active(cons_active(cons_U31(z0, z1)))) -> c2(ACTIVE(active(U31(encArg(z0), encArg(z1)))), ENCARG(cons_active(cons_U31(z0, z1)))) ENCARG(cons_active(cons_active(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(active(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_active(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(active(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_active(cons_U42(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_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_U12(z0)))) -> c2(ACTIVE(mark(U12(encArg(z0)))), ENCARG(cons_mark(cons_U12(z0)))) 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(cons_U21(z0)))) -> c2(ACTIVE(mark(U21(encArg(z0)))), ENCARG(cons_mark(cons_U21(z0)))) ENCARG(cons_active(cons_mark(cons_U31(z0, z1)))) -> c2(ACTIVE(mark(U31(encArg(z0), encArg(z1)))), ENCARG(cons_mark(cons_U31(z0, z1)))) ENCARG(cons_active(cons_mark(cons_U41(z0, z1, z2)))) -> c2(ACTIVE(mark(U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_mark(cons_U42(z0, z1, z2)))) -> c2(ACTIVE(mark(U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_mark(cons_U42(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(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_U12(z0)))) -> c2(ACTIVE(U11(encArg(x0), U12(encArg(z0)))), ENCARG(cons_U11(x0, cons_U12(z0)))) 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(x0, cons_U21(z0)))) -> c2(ACTIVE(U11(encArg(x0), U21(encArg(z0)))), ENCARG(cons_U11(x0, cons_U21(z0)))) ENCARG(cons_active(cons_U11(x0, cons_U31(z0, z1)))) -> c2(ACTIVE(U11(encArg(x0), U31(encArg(z0), encArg(z1)))), ENCARG(cons_U11(x0, cons_U31(z0, z1)))) ENCARG(cons_active(cons_U11(x0, cons_U41(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U41(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U41(z0, z1, z2)))) ENCARG(cons_active(cons_U11(x0, cons_U42(z0, z1, z2)))) -> c2(ACTIVE(U11(encArg(x0), U42(encArg(z0), encArg(z1), encArg(z2)))), ENCARG(cons_U11(x0, cons_U42(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(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_U12(z0), x1))) -> c2(ACTIVE(U11(U12(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_U12(z0), 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_U11(cons_U21(z0), x1))) -> c2(ACTIVE(U11(U21(encArg(z0)), encArg(x1))), ENCARG(cons_U11(cons_U21(z0), x1))) ENCARG(cons_active(cons_U11(cons_U31(z0, z1), x1))) -> c2(ACTIVE(U11(U31(encArg(z0), encArg(z1)), encArg(x1))), ENCARG(cons_U11(cons_U31(z0, z1), x1))) ENCARG(cons_active(cons_U11(cons_U41(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U41(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U41(z0, z1, z2), x1))) ENCARG(cons_active(cons_U11(cons_U42(z0, z1, z2), x1))) -> c2(ACTIVE(U11(U42(encArg(z0), encArg(z1), encArg(z2)), encArg(x1))), ENCARG(cons_U11(cons_U42(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))) S tuples: ACTIVE(U12(tt)) -> c27(MARK(tt)) ACTIVE(U21(tt)) -> c28(MARK(tt)) ACTIVE(U31(tt, z0)) -> c29(MARK(z0)) ACTIVE(U41(tt, z0, z1)) -> c30(MARK(U42(isNat(z1), z0, z1)), U42'(isNat(z1), z0, z1), ISNAT(z1)) ACTIVE(isNat(0)) -> c32(MARK(tt)) ACTIVE(isNat(plus(z0, z1))) -> c33(MARK(U11(isNat(z0), z1)), U11'(isNat(z0), z1), ISNAT(z0)) ACTIVE(plus(z0, s(z1))) -> c36(MARK(U41(isNat(z1), z1, z0)), U41'(isNat(z1), z1, z0), ISNAT(z1)) MARK(isNat(z0)) -> c40(ACTIVE(isNat(z0)), ISNAT(z0)) U11'(mark(z0), z1) -> c48(U11'(z0, z1)) U11'(z0, mark(z1)) -> c49(U11'(z0, z1)) U11'(active(z0), z1) -> c50(U11'(z0, z1)) U11'(z0, active(z1)) -> c51(U11'(z0, z1)) U12'(mark(z0)) -> c52(U12'(z0)) U12'(active(z0)) -> c53(U12'(z0)) ISNAT(mark(z0)) -> c54(ISNAT(z0)) ISNAT(active(z0)) -> c55(ISNAT(z0)) U21'(mark(z0)) -> c56(U21'(z0)) U21'(active(z0)) -> c57(U21'(z0)) U31'(mark(z0), z1) -> c58(U31'(z0, z1)) U31'(z0, mark(z1)) -> c59(U31'(z0, z1)) U31'(active(z0), z1) -> c60(U31'(z0, z1)) U31'(z0, active(z1)) -> c61(U31'(z0, z1)) U41'(mark(z0), z1, z2) -> c62(U41'(z0, z1, z2)) U41'(z0, mark(z1), z2) -> c63(U41'(z0, z1, z2)) U41'(z0, z1, mark(z2)) -> c64(U41'(z0, z1, z2)) U41'(active(z0), z1, z2) -> c65(U41'(z0, z1, z2)) U41'(z0, active(z1), z2) -> c66(U41'(z0, z1, z2)) U41'(z0, z1, active(z2)) -> c67(U41'(z0, z1, z2)) U42'(mark(z0), z1, z2) -> c68(U42'(z0, z1, z2)) U42'(z0, mark(z1), z2) -> c69(U42'(z0, z1, z2)) U42'(z0, z1, mark(z2)) -> c70(U42'(z0, z1, z2)) U42'(active(z0), z1, z2) -> c71(U42'(z0, z1, z2)) U42'(z0, active(z1), z2) -> c72(U42'(z0, z1, z2)) U42'(z0, z1, active(z2)) -> c73(U42'(z0, z1, z2)) S(mark(z0)) -> c74(S(z0)) S(active(z0)) -> c75(S(z0)) PLUS(mark(z0), z1) -> c76(PLUS(z0, z1)) PLUS(z0, mark(z1)) -> c77(PLUS(z0, z1)) PLUS(active(z0), z1) -> c78(PLUS(z0, z1)) PLUS(z0, active(z1)) -> c79(PLUS(z0, z1)) ACTIVE(U11(tt, z0)) -> c26(MARK(U12(isNat(z0))), ISNAT(z0)) ACTIVE(U42(tt, z0, z1)) -> c31(MARK(s(plus(z1, z0))), PLUS(z1, z0)) ACTIVE(isNat(s(z0))) -> c34(MARK(U21(isNat(z0))), ISNAT(z0)) ACTIVE(plus(z0, 0)) -> c35(MARK(U31(isNat(z0), z0)), ISNAT(z0)) MARK(tt) -> c38 MARK(0) -> c47 MARK(U11(z0, z1)) -> c37(ACTIVE(U11(z0, z1)), U11'(mark(z0), z1), MARK(z0)) MARK(U11(U11(z0, z1), x1)) -> c37(ACTIVE(U11(active(U11(mark(z0), z1)), x1)), U11'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U11(tt, x1)) -> c37(ACTIVE(U11(active(tt), x1)), U11'(mark(tt), x1), MARK(tt)) MARK(U11(U12(z0), x1)) -> c37(ACTIVE(U11(active(U12(mark(z0))), x1)), U11'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c37(ACTIVE(U11(active(isNat(z0)), x1)), U11'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c37(ACTIVE(U11(active(U21(mark(z0))), x1)), U11'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c37(ACTIVE(U11(active(U31(mark(z0), z1)), x1)), U11'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U11(U41(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U41(mark(z0), z1, z2)), x1)), U11'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U11(U42(z0, z1, z2), x1)) -> c37(ACTIVE(U11(active(U42(mark(z0), z1, z2)), x1)), U11'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U11(s(z0), x1)) -> c37(ACTIVE(U11(active(s(mark(z0))), x1)), U11'(mark(s(z0)), x1), MARK(s(z0))) MARK(U11(plus(z0, z1), x1)) -> c37(ACTIVE(U11(active(plus(mark(z0), mark(z1))), x1)), U11'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U11(0, x1)) -> c37(ACTIVE(U11(active(0), x1)), U11'(mark(0), x1), MARK(0)) MARK(U11(x0, x1)) -> c37(U11'(mark(x0), x1)) MARK(U12(z0)) -> c39(ACTIVE(U12(z0)), U12'(mark(z0)), MARK(z0)) MARK(U12(U11(z0, z1))) -> c39(ACTIVE(U12(active(U11(mark(z0), z1)))), U12'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U12(tt)) -> c39(ACTIVE(U12(active(tt))), U12'(mark(tt)), MARK(tt)) MARK(U12(U12(z0))) -> c39(ACTIVE(U12(active(U12(mark(z0))))), U12'(mark(U12(z0))), MARK(U12(z0))) MARK(U12(isNat(z0))) -> c39(ACTIVE(U12(active(isNat(z0)))), U12'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U12(U21(z0))) -> c39(ACTIVE(U12(active(U21(mark(z0))))), U12'(mark(U21(z0))), MARK(U21(z0))) MARK(U12(U31(z0, z1))) -> c39(ACTIVE(U12(active(U31(mark(z0), z1)))), U12'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U12(U41(z0, z1, z2))) -> c39(ACTIVE(U12(active(U41(mark(z0), z1, z2)))), U12'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U12(U42(z0, z1, z2))) -> c39(ACTIVE(U12(active(U42(mark(z0), z1, z2)))), U12'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U12(s(z0))) -> c39(ACTIVE(U12(active(s(mark(z0))))), U12'(mark(s(z0))), MARK(s(z0))) MARK(U12(plus(z0, z1))) -> c39(ACTIVE(U12(active(plus(mark(z0), mark(z1))))), U12'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U12(0)) -> c39(ACTIVE(U12(active(0))), U12'(mark(0)), MARK(0)) MARK(U21(z0)) -> c41(ACTIVE(U21(z0)), U21'(mark(z0)), MARK(z0)) MARK(U21(U11(z0, z1))) -> c41(ACTIVE(U21(active(U11(mark(z0), z1)))), U21'(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(U21(tt)) -> c41(ACTIVE(U21(active(tt))), U21'(mark(tt)), MARK(tt)) MARK(U21(U12(z0))) -> c41(ACTIVE(U21(active(U12(mark(z0))))), U21'(mark(U12(z0))), MARK(U12(z0))) MARK(U21(isNat(z0))) -> c41(ACTIVE(U21(active(isNat(z0)))), U21'(mark(isNat(z0))), MARK(isNat(z0))) MARK(U21(U21(z0))) -> c41(ACTIVE(U21(active(U21(mark(z0))))), U21'(mark(U21(z0))), MARK(U21(z0))) MARK(U21(U31(z0, z1))) -> c41(ACTIVE(U21(active(U31(mark(z0), z1)))), U21'(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(U21(U41(z0, z1, z2))) -> c41(ACTIVE(U21(active(U41(mark(z0), z1, z2)))), U21'(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(U21(U42(z0, z1, z2))) -> c41(ACTIVE(U21(active(U42(mark(z0), z1, z2)))), U21'(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(U21(s(z0))) -> c41(ACTIVE(U21(active(s(mark(z0))))), U21'(mark(s(z0))), MARK(s(z0))) MARK(U21(plus(z0, z1))) -> c41(ACTIVE(U21(active(plus(mark(z0), mark(z1))))), U21'(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(U21(0)) -> c41(ACTIVE(U21(active(0))), U21'(mark(0)), MARK(0)) MARK(U31(z0, z1)) -> c42(ACTIVE(U31(z0, z1)), U31'(mark(z0), z1), MARK(z0)) MARK(U31(U11(z0, z1), x1)) -> c42(ACTIVE(U31(active(U11(mark(z0), z1)), x1)), U31'(mark(U11(z0, z1)), x1), MARK(U11(z0, z1))) MARK(U31(tt, x1)) -> c42(ACTIVE(U31(active(tt), x1)), U31'(mark(tt), x1), MARK(tt)) MARK(U31(U12(z0), x1)) -> c42(ACTIVE(U31(active(U12(mark(z0))), x1)), U31'(mark(U12(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c42(ACTIVE(U31(active(isNat(z0)), x1)), U31'(mark(isNat(z0)), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c42(ACTIVE(U31(active(U21(mark(z0))), x1)), U31'(mark(U21(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c42(ACTIVE(U31(active(U31(mark(z0), z1)), x1)), U31'(mark(U31(z0, z1)), x1), MARK(U31(z0, z1))) MARK(U31(U41(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U41(mark(z0), z1, z2)), x1)), U31'(mark(U41(z0, z1, z2)), x1), MARK(U41(z0, z1, z2))) MARK(U31(U42(z0, z1, z2), x1)) -> c42(ACTIVE(U31(active(U42(mark(z0), z1, z2)), x1)), U31'(mark(U42(z0, z1, z2)), x1), MARK(U42(z0, z1, z2))) MARK(U31(s(z0), x1)) -> c42(ACTIVE(U31(active(s(mark(z0))), x1)), U31'(mark(s(z0)), x1), MARK(s(z0))) MARK(U31(plus(z0, z1), x1)) -> c42(ACTIVE(U31(active(plus(mark(z0), mark(z1))), x1)), U31'(mark(plus(z0, z1)), x1), MARK(plus(z0, z1))) MARK(U31(0, x1)) -> c42(ACTIVE(U31(active(0), x1)), U31'(mark(0), x1), MARK(0)) MARK(U31(x0, x1)) -> c42(U31'(mark(x0), x1)) MARK(U41(z0, z1, z2)) -> c43(ACTIVE(U41(z0, z1, z2)), U41'(mark(z0), z1, z2), MARK(z0)) MARK(U41(U11(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U11(mark(z0), z1)), x1, x2)), U41'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U41(tt, x1, x2)) -> c43(ACTIVE(U41(active(tt), x1, x2)), U41'(mark(tt), x1, x2), MARK(tt)) MARK(U41(U12(z0), x1, x2)) -> c43(ACTIVE(U41(active(U12(mark(z0))), x1, x2)), U41'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U41(isNat(z0), x1, x2)) -> c43(ACTIVE(U41(active(isNat(z0)), x1, x2)), U41'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U41(U21(z0), x1, x2)) -> c43(ACTIVE(U41(active(U21(mark(z0))), x1, x2)), U41'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(U31(mark(z0), z1)), x1, x2)), U41'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U41(U41(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U41(mark(z0), z1, z2)), x1, x2)), U41'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U41(U42(z0, z1, z2), x1, x2)) -> c43(ACTIVE(U41(active(U42(mark(z0), z1, z2)), x1, x2)), U41'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U41(s(z0), x1, x2)) -> c43(ACTIVE(U41(active(s(mark(z0))), x1, x2)), U41'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U41(plus(z0, z1), x1, x2)) -> c43(ACTIVE(U41(active(plus(mark(z0), mark(z1))), x1, x2)), U41'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U41(0, x1, x2)) -> c43(ACTIVE(U41(active(0), x1, x2)), U41'(mark(0), x1, x2), MARK(0)) MARK(U41(x0, x1, x2)) -> c43(U41'(mark(x0), x1, x2)) MARK(U42(z0, z1, z2)) -> c44(ACTIVE(U42(z0, z1, z2)), U42'(mark(z0), z1, z2), MARK(z0)) MARK(U42(U11(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U11(mark(z0), z1)), x1, x2)), U42'(mark(U11(z0, z1)), x1, x2), MARK(U11(z0, z1))) MARK(U42(tt, x1, x2)) -> c44(ACTIVE(U42(active(tt), x1, x2)), U42'(mark(tt), x1, x2), MARK(tt)) MARK(U42(U12(z0), x1, x2)) -> c44(ACTIVE(U42(active(U12(mark(z0))), x1, x2)), U42'(mark(U12(z0)), x1, x2), MARK(U12(z0))) MARK(U42(isNat(z0), x1, x2)) -> c44(ACTIVE(U42(active(isNat(z0)), x1, x2)), U42'(mark(isNat(z0)), x1, x2), MARK(isNat(z0))) MARK(U42(U21(z0), x1, x2)) -> c44(ACTIVE(U42(active(U21(mark(z0))), x1, x2)), U42'(mark(U21(z0)), x1, x2), MARK(U21(z0))) MARK(U42(U31(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(U31(mark(z0), z1)), x1, x2)), U42'(mark(U31(z0, z1)), x1, x2), MARK(U31(z0, z1))) MARK(U42(U41(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U41(mark(z0), z1, z2)), x1, x2)), U42'(mark(U41(z0, z1, z2)), x1, x2), MARK(U41(z0, z1, z2))) MARK(U42(U42(z0, z1, z2), x1, x2)) -> c44(ACTIVE(U42(active(U42(mark(z0), z1, z2)), x1, x2)), U42'(mark(U42(z0, z1, z2)), x1, x2), MARK(U42(z0, z1, z2))) MARK(U42(s(z0), x1, x2)) -> c44(ACTIVE(U42(active(s(mark(z0))), x1, x2)), U42'(mark(s(z0)), x1, x2), MARK(s(z0))) MARK(U42(plus(z0, z1), x1, x2)) -> c44(ACTIVE(U42(active(plus(mark(z0), mark(z1))), x1, x2)), U42'(mark(plus(z0, z1)), x1, x2), MARK(plus(z0, z1))) MARK(U42(0, x1, x2)) -> c44(ACTIVE(U42(active(0), x1, x2)), U42'(mark(0), x1, x2), MARK(0)) MARK(U42(x0, x1, x2)) -> c44(U42'(mark(x0), x1, x2)) MARK(s(U11(z0, z1))) -> c45(ACTIVE(s(active(U11(mark(z0), z1)))), S(mark(U11(z0, z1))), MARK(U11(z0, z1))) MARK(s(tt)) -> c45(ACTIVE(s(active(tt))), S(mark(tt)), MARK(tt)) MARK(s(U12(z0))) -> c45(ACTIVE(s(active(U12(mark(z0))))), S(mark(U12(z0))), MARK(U12(z0))) MARK(s(isNat(z0))) -> c45(ACTIVE(s(active(isNat(z0)))), S(mark(isNat(z0))), MARK(isNat(z0))) MARK(s(U21(z0))) -> c45(ACTIVE(s(active(U21(mark(z0))))), S(mark(U21(z0))), MARK(U21(z0))) MARK(s(U31(z0, z1))) -> c45(ACTIVE(s(active(U31(mark(z0), z1)))), S(mark(U31(z0, z1))), MARK(U31(z0, z1))) MARK(s(U41(z0, z1, z2))) -> c45(ACTIVE(s(active(U41(mark(z0), z1, z2)))), S(mark(U41(z0, z1, z2))), MARK(U41(z0, z1, z2))) MARK(s(U42(z0, z1, z2))) -> c45(ACTIVE(s(active(U42(mark(z0), z1, z2)))), S(mark(U42(z0, z1, z2))), MARK(U42(z0, z1, z2))) MARK(s(s(z0))) -> c45(ACTIVE(s(active(s(mark(z0))))), S(mark(s(z0))), MARK(s(z0))) MARK(s(plus(z0, z1))) -> c45(ACTIVE(s(active(plus(mark(z0), mark(z1))))), S(mark(plus(z0, z1))), MARK(plus(z0, z1))) MARK(s(0)) -> c45(ACTIVE(s(active(0))), S(mark(0)), MARK(0)) MARK(s(z0)) -> c45(S(mark(z0)), MARK(z0)) MARK(plus(z0, x1)) -> c46(ACTIVE(plus(z0, mark(x1))), PLUS(mark(z0), mark(x1)), MARK(z0), MARK(x1)) MARK(plus(x0, z1)) -> c46(ACTIVE(plus(mark(x0), z1)), PLUS(mark(x0), mark(z1)), MARK(x0), MARK(z1)) MARK(plus(x0, U11(z0, z1))) -> c46(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)) -> c46(ACTIVE(plus(mark(x0), active(tt))), PLUS(mark(x0), mark(tt)), MARK(x0), MARK(tt)) MARK(plus(x0, U12(z0))) -> c46(ACTIVE(plus(mark(x0), active(U12(mark(z0))))), PLUS(mark(x0), mark(U12(z0))), MARK(x0), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(ACTIVE(plus(mark(x0), active(isNat(z0)))), PLUS(mark(x0), mark(isNat(z0))), MARK(x0), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(ACTIVE(plus(mark(x0), active(U21(mark(z0))))), PLUS(mark(x0), mark(U21(z0))), MARK(x0), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(ACTIVE(plus(mark(x0), active(U31(mark(z0), z1)))), PLUS(mark(x0), mark(U31(z0, z1))), MARK(x0), MARK(U31(z0, z1))) MARK(plus(x0, U41(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U41(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U41(z0, z1, z2))), MARK(x0), MARK(U41(z0, z1, z2))) MARK(plus(x0, U42(z0, z1, z2))) -> c46(ACTIVE(plus(mark(x0), active(U42(mark(z0), z1, z2)))), PLUS(mark(x0), mark(U42(z0, z1, z2))), MARK(x0), MARK(U42(z0, z1, z2))) MARK(plus(x0, s(z0))) -> c46(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))) -> c46(ACTIVE(plus(mark(x0), active(plus(mark(z0), mark(z1))))), PLUS(mark(x0), mark(plus(z0, z1))), MARK(x0), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c46(ACTIVE(plus(mark(x0), active(0))), PLUS(mark(x0), mark(0)), MARK(x0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(tt), mark(x1))), PLUS(mark(tt), mark(x1)), MARK(tt), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(ACTIVE(plus(active(U12(mark(z0))), mark(x1))), PLUS(mark(U12(z0)), mark(x1)), MARK(U12(z0)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(ACTIVE(plus(active(isNat(z0)), mark(x1))), PLUS(mark(isNat(z0)), mark(x1)), MARK(isNat(z0)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(ACTIVE(plus(active(U21(mark(z0))), mark(x1))), PLUS(mark(U21(z0)), mark(x1)), MARK(U21(z0)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(ACTIVE(plus(active(U31(mark(z0), z1)), mark(x1))), PLUS(mark(U31(z0, z1)), mark(x1)), MARK(U31(z0, z1)), MARK(x1)) MARK(plus(U41(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U41(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U41(z0, z1, z2)), mark(x1)), MARK(U41(z0, z1, z2)), MARK(x1)) MARK(plus(U42(z0, z1, z2), x1)) -> c46(ACTIVE(plus(active(U42(mark(z0), z1, z2)), mark(x1))), PLUS(mark(U42(z0, z1, z2)), mark(x1)), MARK(U42(z0, z1, z2)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(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)) -> c46(ACTIVE(plus(active(plus(mark(z0), mark(z1))), mark(x1))), PLUS(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1)), MARK(x1)) MARK(plus(0, x1)) -> c46(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, U12_1, isNat_1, U21_1, U31_2, U41_3, U42_3, s_1, plus_2 Defined Pair Symbols: ACTIVE_1, MARK_1, U11'_2, U12'_1, ISNAT_1, U21'_1, U31'_2, U41'_3, U42'_3, S_1, PLUS_2, ENCARG_1, ENCODE_ACTIVE_1, ENCODE_U11_2, ENCODE_MARK_1, ENCODE_U12_1, ENCODE_ISNAT_1, ENCODE_U21_1, ENCODE_U31_2, ENCODE_U41_3, ENCODE_U42_3, ENCODE_S_1, ENCODE_PLUS_2 Compound Symbols: c27_1, c28_1, c29_1, c30_3, c32_1, c33_3, c36_3, c40_2, c48_1, c49_1, c50_1, c51_1, c52_1, c53_1, c54_1, c55_1, c56_1, c57_1, c58_1, c59_1, c60_1, c61_1, c62_1, c63_1, c64_1, c65_1, c66_1, c67_1, c68_1, c69_1, c70_1, c71_1, c72_1, c73_1, c74_1, c75_1, c76_1, c77_1, c78_1, c79_1, c26_2, c31_2, c34_2, c35_2, c38, c47, c2_2, c3_2, c3_1, c4_3, c4_2, c5_2, c6_2, c7_2, c8_3, c8_2, c9_4, c9_3, c10_4, c10_3, c11_2, c12_3, c12_2, c37_3, c37_1, c39_3, c41_3, c42_3, c42_1, c43_3, c43_1, c44_3, c44_1, c45_3, c45_2, c46_4, c_1, c1_1